There's definitely a political aspect to this question as well as a legal one.
For the political aspect, Special Counsel Robert Mueller wants verbal testimony from Trump because it allows for a better evaluation of the veracity of a witness's claims and it allows him to follow-up in real-time. Even if Mueller suspects Trump will commit perjury under these conditions, it's not a perjury trap anymore than a prostitution sting is entrapment. Mueller is looking into a wide array of contacts during the campaign by high ranking campaign officials, advisors, and Trump's kids. Not to mention the suspected obstruction of justice charge relating to the Comey firing. Mueller isn't bringing Trump in to create a perjury charge, but to testify about suspected crimes, some of which personally involve Trump. It may be an interview with a high risk of committing perjury, but that doesn't make it improper in the slightest.
I think this is distinct from the legal aspect of your question, though, as to what exactly constitutes a perjury trap. The perjury trap was written about extensively in the University of Pennsylvania Law Review in 1981. To summarize, a "perjury trap" is when the prosecutor suspects a witness of criminal activity, but there is not sufficient evidence to prove a substantive crime, but there is sufficient evidence to prove a witness's false denials. You can read many examples in the paper itself, but I'll quote one such example to show that there needs to be a difference between an "honest investigation" and "intentionally setting up the witness to perjure himself":
Assume that during an investigation into political corruption,
government investigators using a court-ordered wiretap secretly
overhear a telephone conversation between a person named White, leader
of a local political party, and an acquaintance of his named Singer, a
real estate developer under scrutiny by the district attorney's office
in connection with alleged pay-offs to housing inspectors. A
transcript of a portion of the ten-minute telephone conversation
WHITE: Get to the point.
SINGER: Let me ask you this. The D.A. says I gave money to building
people. I'm being looked at very closely.
WHITE: Who's talking?
SINGER: I don't know. That's one of the things I wanted to ask you.
Who it is and whether this thing can be worked out. You don't know
what it's doing to me.
WHITE: Do you have a lawyer?
SINGER: I haven't talked to one yet.
WHITE: Well, you should get a lawyer who knows his way around, I mean
a lawyer who can talk to these people.
SINGER: Knows which people?
WHITE: A lawyer who can straighten things out, who knows the D.A. Why
don't you talk to my brother Al. He's been there before. He knows how
to handle these things. Talk to him. He may be able to help you. If
anybody can quash it with the D.A., he can.
Four months later, White was subpoenaed to appear before a grand jury.
Prior to his appearance, and represented by counsel, White was
informally advised by the prosecutor that the grand jury was
conducting an investigation into official corruption, including the
crimes of bribery, conspiracy, and official misconduct, and that it
desired to question White in that regard. White was advised by the
prosecutor that he was not a target of the investigation, that he
could refuse to answer any questions by invoking his fifth amendment
privilege, and that in the event he chose to invoke the privilege, the
grand jury would compel his testimony by conferring transactional
immunity upon him. White's attorney stated that White would cooperate
fully with the grand jury but would request immunity. The prosecutor
After taking the oath, White was questioned by the prosecutor.
Following preliminary background questions, White was asked whether he
had ever intervened on anyone's behalf to influence official actions
in a legal proceeding. White stoutly denied that he had ever done so.
White then was asked whether he knew a person named Singer, and
whether he had talked to him recently. White said he had. The
prosecutor then engaged White in the following interrogation:
Q. You say that Singer asked you for advice?
A. Yes, he asked me for advice on a legal matter and I told him I
couldn't give him any advice.
Q. Did he tell you what kind of legal matter it was?
Q. Did he ask you anything else?
A. He asked me if there was anything I could do for him.
Q. What did you tell him?
A. I told him that I could not give him legal advice; that if he
wanted legal advice he should go to see a lawyer.
Q. Did he say anything else?
A. He asked me if I knew any lawyers. I told him my brother was a
lawyer and that if he needed legal advice he could speak to my
brother. That's as far as I can recall the conversation. It lasted
only a few minutes.
Q. Did you tell Singer that he should get a lawyer who could influence
A. I did not.
Q. Did you tell Singer that he should get a lawyer who could fix
things with the D.A.?
A. Absolutely not.
Q. Did you tell Singer that your brother could quash things with the
On the basis of this testimony, the grand jury indicted White on three
counts of perjury for his denials in response to the last three
questions. The evidence against White was the authenticated tape
recording of his telephone conversation with Singer previously
introduced in evidence before the grand jury.
Here, the prosecutor immunized White to give the appearance that he was investigating more serious crimes, but the prosecutor's questions largely tracked the transcript of the telephone conversation, whether the witness had said something the grand jury and prosecutor had already secretly knew he had said. There is no indication that truthful answers to these questions would have materially advanced the grand jury's investigation into the political corruption (alleged payoffs to housing inspectors).
Thus, there most certainly is a "perjury trap" in regards to perhaps "playing upon the ambiguity of language and the hazy memory of the witness as against the clarity of the prosecutor's meaning to the grand jurors and their immediate recall of the recorded conversation", but this is materially different than questioning someone in regards to a criminal investigation where the subject has a propensity to lie about matters of the investigation.