Hull owners Assem and Ehab Allam have refused to confirm whether or not they suspended Barmby last week over comments the 38-year-old has made in recent weeks about the club's finances.
But it is understood Barmby has now been removed from his position following a meeting with the Allams on Tuesday.
Hull head of football operations Adam Pearson was sacked last week.
Pearson, 47, who spent six years as chairman of the club from 2001, had his consultancy role terminated "without notice and without compensation".
The Allams have since refused to respond to speculation that Barmby had been suspended for comments made about the club's financial situation.
Barmby has insisted on several occasions in recent weeks that team strengthening was vital during the summer if Hull were to mount a serious promotion challenge and that he would be expecting financial support from the board.
Ehab Allam has said he and his father had every right to be disappointed that the Tigers had failed to finish in the play-offs this season due to the club's ?17million wage bill.
He has also said he would have sanctioned the signing of striker Billy Sharp, who was available in January and later joined Southampton for ?1.8million, at a cost of between ?30-40,000 a week until the end of the season.
Hull appeared on course for the play-offs until a run of five straight defeats in March derailed their challenge and they finished seven points adrift of the top six.