HITC Sport understands that the Cherries are unlikely to raise their offer
Bournemouth are looking to bring in a number of new attacking players this month and have already landed Juan Iturbe from Roma, but the return of Grabban has long been on Eddie Howe's wish-list.
Howe remains a huge fan of Grabban following his previous spell at Dean Court, and they came very close to landing him during the last window but the deal fell through with just hours to go and the player in Bournemouth ready to sign on the dotted line.
He has made it clear to Norwich that he does not want to stay at Carrow Road and a return to Bournemouth has always been his move of choice, despite interest from a number of Championship clubs including Derby County and Sheffield Wednesday.
Bournemouth have been in contact with Norwich for weeks and believed that they had made the right offer which HITC Sport understands was £7million plus a further £1million in add-ons.
However, Norwich have told Bournemouth that they need to up their offer if they want to re-sign Grabban. It is now unclear whether Bournemouth will return with an improved offer as they are in the market for other strikers.