Several championship clubs are believed to be keeping a close eye on his situation at Oakwell.
The 28-year-old has struggled to hold down a regular role this season, sparking speculation that he could soon be on the move.
Dawson will also see his current contract expire at the end of the campaign, casting him into the free agent pool.
It is possible that he will never reach that point, with a switch in the New Year mooted.
The former Leyton Orient man is a combative box-to-box midfielder and was heavily linked with a step up into the Championship prior to joining Barnsley in January 2012.
He has not looked out of place at that level and he may be offered the opportunity to extend his stay in the second tier.