Pearson, who spent six years as chairman of the club from 2001, has had his consultancy role terminated "without notice and without compensation". The Allams refused to respond to speculation that Barmby had been suspended for comments made about the club's financial situation and have left fans in the dark as to the 38-year-old's future.
A club statement issued on Tuesday morning read: "When we acquired the football club we made it clear we would run it in accordance with sound and proper business principles and procedures. We have not and will not deviate from those principles."
It continued: "Therefore although we fully appreciate the supporters' and media's desire for information we cannot comment on the manager's position at the present time. We will however provide further information when we are able to do so.
"Having listened to media speculation today over funds not being available in the January transfer window, we reiterate that funds were available as previously stated by us. We also confirm the club has terminated the consultancy agreement with Adam Pearson without notice and without compensation.
"We are also aware of speculation about the club being up for sale. We can categorically confirm there is no truth in that rumour and we are fully committed to Hull City and its future."
The majority of fans have already expressed their outrage at Barmby's treatment on local radio, while a small minority believe the former Tigers player has antagonised the owners. Barmby has repeatedly claimed Hull need financial support from the board if they are to mount a serious promotion challenge next term.
Pearson quit as Leeds United's commercial director in 2001 to buy Hull and take over as chairman while they were in administration and languishing at the bottom end of the old Third Division.
In 2007 he resigned to make way for new owner Paul Duffen, but returned as chairman again in November 2009 and then became head of football operations under new owner Russell Bartlett after the club had been relegated from the Barclays Premier League in 2010.
Pearson stayed on in his role when the Allam family took control from Bartlett in December 2010.