Sunderland are said to be interested in Tomkins, but they will have to spend a considerable amount of funds if they are to land the centre-back.
West Ham rate the 26-year-old highly, and they are not willing to lose him on the cheap.
Tomkins’ future at West Ham has come into doubt, because he has found it harder to make first team appearances this season.
The Hammers increased their defensive options over the summer by recruiting Angelo Ogbonna, and Tomkins appears to be third choice centre back now.
Sunderland manager Allardyce knows Tomkins well, having worked with him at Upton Park, earlier in their respective careers.
Sunderland are also said to be interested in signing James Collins from West Ham, who would be a considerably cheaper option.
Tomkins has played 18 times for the Hammers in all competition this season, but his chances have been increased due to West Ham's failure to keep players off the treatment table so far.