Chairman Huw Jenkins says the chances of midfielder Andy Robinson staying at Swansea are "50-50".
Andy Robinson has one year left on his current Swans deal
"Andy's agent and I are quite a way apart in what we think the level of his contract should be," said Jenkins.
"It's in the balance, but Andy can't go anywhere. He's under contract and doesn't have a get-out clause like Sam Ricketts if a certain bid is made."
Championship sides Cardiff and Southend are interested in Robinson, 26, who has a year to run on his Swansea deal.
The player said last week that he was keen to sign an extended contract offer that would take him to June 2008.
The Swans turned down a £150,000 offer from Southend last month.
No new bid has yet come in, but the Shrimpers are expected to come back for Robinson, while Cardiff's interest could complicate matters.
Andy gave everything to the club last season
Swansea manager Kenny Jackett
The Swans are already smarting from the loss of transfer target Roger Johnson to Cardiff, while Sam Ricketts has completed a move from the Liberty Stadium to Hull.
Robinson, who had a brief spell at Tranmere, signed for the Swans in 2003 after arriving from Merseyside non-League football on trial.
He went on to win the Player of the Year award and has been a consistent performer in the Swansea midfield ever since.
Robinson has chalked up his fair share of goals along the way, including 18 last season in all competitions.
"I am keen to keep Andy at the club beyond his current contract," said Swansea manager Kenny Jackett last week.
"I'm a firm believer in rewarding players for their efforts.
"Andy gave everything to the club last season and was a top performer on a consistent basis, his commitment and enthusiasm were impressive.
"He has been offered an improved contract that will keep him at the club until June 2008 and we are hoping to finalise matters."