Burgess is in his second season with the four times European champions, but has been forced to share the No 9 jersey with Jean-Marc Doussain. It was Doussain who started in the French Championship final in Paris last year, with Burgess coming on in the second half.
The Melbourne Rebels and the Brumbies are chasing his signature for 2014, while Michael Cheika's Waratahs are also understood to have expressed interest in their former player. The Australian Rugby Union has been in informal contact with Burgess about a possible return, which would be dependent on Toulouse agreeing to the release.
Wallaby coach Robbie Deans approached Burgess to ask him to go on stand-by for the Wallabies' Spring Tour last year and Burgess revealed Deans had also expressed interest in him possibly playing a role against the Lions.
"I'm tempted, I'll say that. I haven't ruled it out or in," Burgess was reported as having told a newspaper earlier in the season. "The Lions are a big thing for any rugby player, so I'm tempted.''
The Wallabies struggled at scrum half when Will Genia was injured last year and have no outstanding candidate to fill in for their No 9 wizard if his injured knee causes him further problems. Burgess relinquished his spot as Genia's understudy when he left for France, but neither Nick Phipps nor Brett Sheehan were convincing in their attempts to fill in.