Larsson is a free agent at the end of the season and, with Sunderland fighting for Premier League survival, head coach Guy Poyet has put talks over a new deal on hold.
The Sweden international midfielder remains in limbo after his representative Per Jonsson admitted that a decision either way is unlikely to be made this month.
"I met Gus Poyet in December and he wanted to prolong Seb's stay," Jonsson told the Sunderland Echo.
"But at that point, they were adrift, so we agreed that none of the parties want to commit to anything at that stage.
"We wanted to see if they were going to stay in the Premier League. Teams that are relegated obviously need to change their wage structure.
"After that, there have not been any more talks.
"In a month's time, we will know what the situation is. I don't see any progress until that stage.
"He is open to staying in the Premier League - whether that is Sunderland or someone else.
"As a Bosman, he will obviously have lots of clubs looking at him, particularly with his international record."
The 28-year-old has made over 100 appearances in all competitions for Sunderland since arriving at the Stadium of Light on a free transfer from Birmingham City in 2011.
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