No, there is no announced timeline, yet.
CNN, however, provides informed speculation on a timeline. It's a bit dated, the article was published November 7th, but it still holds up. In fact, the article has the first open hearing this week, when they actually started open hearings last week. The timetable, as speculated by CNN is:
After weeks of private depositions, the next phases of the House impeachment proceedings could conclude before 2020.
Schiff has announced that three witnesses would testify next week, and Democratic lawmakers expect at least one more week of public hearings before his panel likely to follow on the week of November 18.
The House is then scheduled to take a recess for Thanksgiving week, giving time for Schiff's committee — along with House Oversight and House Foreign Affairs — to finish a report detailing their findings and recommendations of their investigation.
At that point, the House Judiciary Committee would take the lead on the impeachment push — potentially in the first week of December. Democratic sources expect that committee to have a public hearing, possibly in that week, before it votes on articles of impeachment. That vote could occur in committee in the first or second week of December, the sources said.
If that timeline is followed, that would set up a full House vote to impeach Trump on the week of December 16 — a historic vote that could come 21 years after President Bill Clinton was impeached by the House on December 19, 1998.
The article goes on to express that the timetable is not set in stone by quoting Democrats who have effective control over the timetable:
Still, Democrats are wary about specifying a timeframe.
"I'm not going to speculate on a timeline," House Judiciary Chairman Jerry Nadler said on CNN Thursday. "We want to finish the process as expeditiously as possible and thoroughly ... that the American people see what the evidence is - what the contradictory evidence is if any - and if it's going to be done, it's got to be done right and whatever time required it takes."
House Majority Leader Steny Hoyer told lawmakers this week they should expect to be in session the week of December 16. Hoyer cited the need to pass spending bills to avoid a government shutdown, but it's also possible the time will be used to take up impeachment.