It's been reported several times that several groups, individuals and institutions have been paid off by the Qatari government for favorable press treatment in the West. For example Wikipedia has this to say about Brookings
The Qatari government was named by The New York Times as "the single biggest foreign donor to Brookings", having reportedly made a $14.8 million, four-year contribution in 2013. A former visiting fellow at a Brookings affiliate in Qatar reportedly said that "he had been told during his job interview that he could not take positions critical of the Qatar government in papers".
Is there a good or definitive listing of press that has taken Qatari money?