HITC Sport understands that the Bournemouth target will not return to club until next week.
The 27-year-old left Norwich's team hotel ahead of their League Cup clash with Rotherham United, after he learned of a third bid from Bournemouth being rejected.
Now Bournemouth want him back and have now made three unsuccessful bids to land him – as revealed by HITC Sport - but Norwich have rejected them all.
Following Grabban's decision to leave the team hotel on Tuesday, Norwich informed him on Wednesday that he should not return until next week.
Norwich themselves are considering their options with Bournemouth likely to make another offer. They have seen a third bid of their own for Benik Afobe rejected, whilst they have also been linked to Glenn Murray, Dwight Gayle and Charlie Austin in recent weeks.