The Tractor Boys have been given permission to hold talks with the former England Under 21 international.
Though the two clubs have yet to agree on a fee, reports suggest Newcastle are willing to accept £2.5million for Ameobi.
"Newcastle have given us permission to talk to the lad and we have been in contact with his agent," Town boss Jim Magilton told the East Anglian Daily Times.
"I leave the initial talks to Derek Bowden and if we get to a point of agreeing, then I will sit down and look him in the eye and see if he has the desire I'm looking for.
"Newcastle are looking to offload the boy as he is in the last year of his contract.
"He is a lad with immense promise, but at 26-years-old he needs to start fulfilling that promise.
"He didn't have a fantastic time on loan at Stoke, but he was probably hampered by an injury.
"It is up to him now. If he wants to hang around Newcastle and then be a free agent then fine, but if he wants to come here and show a desire to play at Championship level then we would be a club interested in him."