Ince, who has a year to run on his contract at Hull, spent last season on loan at Derby where he played under incoming Newcastle manager Steve McClaren.
The 23-year-old impressed in his spell at the iPro Stadium, netting 11 goals in 18 games, and the Rams are now ready to break their transfer record to sign him.
Derby’s previous record signing, Wales striker Robert Earnshaw, cost the club £3.5m from Norwich City in 2007 but any fee for Ince is expected to exceed that.
Former Derby manager McClaren is keen to reunite with the player at Newcastle after being impressed by him last season and he is ready to rival his old club for the England U21 international’s signature.
McClaren is determined to turn around Newcastle’s fortunes and is targeting a top-eight finish and a trophy after signing a three-year deal at St James’ Park.
The former England manager knows investment in the squad is needed and is confident owner Mike Ashley is ready to back him in the transfer market.
McClaren said: “If we can get the right recruitment and we get the right resources as well, this club can take off.
“There is a lot of work to do, but the club has made it clear about wanting success, and I would not have come here if I didn’t believe they were serious.”