Tiger's chairman Adam Pearson confirmed Hull's approach for Elliott, who will be 24 later this month, on Monday.
Pearson said: "We have made a bid for Elliott and I expect him to be here on Monday."
Motherwell have reluctantly allowed Elliott, who has scored 22 goals in 50 appearances in the Scottish Premier League, permission to talk to Hull.
Well are currently in administration and with Elliott's contract up at the end of the forthcoming season, they may be unable to turn down Hull's offer.
But Brian Jackson of the administrators PKF said that the deal was not yet done.
"Stuart Elliott has been given the all-clear to talk to Hull City and he intends to do so.
However, he added: "Reports that a deal has been struck are premature.
"Elliott is still not sure himself what he wants."
Elliott himself revealed on Monday night that he would like to stay with Motherwell if they could afford to keep him.
He said: "I would be happy to accept if Motherwell made me an offer to stay.
"But the club are on a bit of a downer, what with the financial situation.
"I have spoken with my agent, the boss (Terry Butcher) and my family and talks with Hull are ongoing.
"Nothing has been decided yet but I have to do what's best for my family."
If the deal goes through he will link up at Boothferry Park with former Motherwell defender Greg Strong who left Fir Park in May.
Hull have also targeted Crewe left-back Shaun Smith and hope to clinch a double deal.