The Evening Chronicle reports that United had a £4.2million bid for the 21-year-old defender was rejected by the Tractor Boys.
Freddy Shepherd is unlikley to budge too much on the fee, but with Bramble out of contract at the end of next season and refusing to sign a contract to stay at Ipswich.
Bramble himself is said to be keen on a move upto St James Park, where he would team up with former teammate Kieron Dyer.
Any discussions over a Bramble move may take a while to take place, for him to be eligible for the Champions League qualifying phases though he would need to be registered before August 08th.