Wigan are currently the only club with a bid on the table for the 30 year old, thought to be worth around รยฃ1.5m plus add-ons.
But the Tigers could yet scupper the move, after they were told by Berry that a fee of รยฃ2m would be enough to take Scotland to the KC Stadium.
However, Berry still expects the deal to go through with the Latics in the next few days, which would see the Trinidad & Tobago frontman re-unite with former Swans boss Roberto Martinez.
Scotland scored 24 times last season, but with his contract set to expire next summer, he would be allowed to agree a deal at a new club as early as next January – and no fee would be due.
“I spoke to Brian Horton and he asked me what the bottom-line price would be for Jason,” Berry told the Hull Daily Mail.
“I said I thought a fee of รยฃ2million would probably be enough to get him in.
“My belief was that he’d be ideal for Hull, but I expect the Wigan deal to go ahead now.”