The 31-year-old has been a regular in the Newcastle defence in recent seasons, but new coach Steve McClaren looks set to move on with new ideas.
Anderlecht defender Chancel Mbemba has already signed for the Magpies this summer, pending a work permit, and they are in the market for another stopper.
Now Williamson is on the lookout for a new club, although he does have one year remaining on his current deal.
Williamson is attracting interest from the Premier League and the Championship. Aston Villa and his former boss Alan Pardew, at Crystal Palace, are both understood to be keeping tabs on his situation, whilst the likes of Sheffield Wednesday, Leeds United and Hull City are also believed to be keen.
The Daily Mirror were among the first to link Leeds with an approach for the experienced centre-half, but they have landed Sol Bamba on a permanent basis while Villa have already bolstered their defensive ranks with the addition of Micah Richards – although they have lost Ron Vlaar to free agency.
Williamson has played over 150 times for Newcastle since joining from Portsmouth in 2010.