The center half is being linked to Merseyside club Everton, who may sell Jarrad Branthwaite.
If the latter moves to Manchester United, ex-Tigers boss Steve Bruce believes Greaves is the ideal replacement.
HullLive quote Bruce as saying: "The kid (Jarrad) Branthwaite, have they turned down £45m?
“He was at Carlisle, and I should have taken him - he was on our doorstep at Newcastle and he was only £1.5m or £2m when he went to Everton.
“He's flourished and he's now at £45m all of a sudden? The thing is, he's been there and done it in the Premier League whereas the boy Greaves (has not).
“It will probably take a cheque, probably north of £20m now to even consider it I would have thought."
