According to The Telegraph, the Tractor Boys are considering an approach for the centre-back ahead of their return to the Premier League.
Kieran McKenna is looking to strengthen his side after the Suffolk outfit gained promotion to the top flight with a second place finish in the Championship.
Greaves impressed many with his performances for Hull last year, earning a lot of plaudits as the team finished seventh in the standings.
This has led to reports that West Ham and Everton are also interested in signing the defender, raising doubts over his future at the MKM Stadium.
Carlton Palmer gives Jacob Greaves transfer verdict
Carlton Palmer believes that Greaves’ future could be tied to the transfer situation surrounding Everton’s Jarrad Branthwaite, who is wanted by Manchester United.
He has also predicted that any deal involving the 23-year-old could cost between £20 and 25 million.
“As you can imagine, Ipswich Town have been linked with a whole host of players, having been promoted to the Premier League,” Palmer told Football League World.
“Obviously they want to strengthen their squad.
“One of the players they have been linked with is Hull City centre-back Jacob Greaves.
