The 33-year-old City winger rejoined his former club on loan until the end of December with a view to making the move back to Wales permanent in January.
However,Swans chairman Huw Jenkins has revealed that he is unsure whether Trundle will be offered a permanent deal at the end of the loan spell has he not been a regular starter for Paulo Sousa's side in recent times.
"It's been difficult for Lee," Jenkins told the South Wales Evening Post.
"The way we play and the shape we play, plus the fact we have been on such a good run, has probably hampered Lee's progress.
"We tend to revert to two up front when we are behind in games and, as it stands, Lee has been unlucky since he came back. But I think he understands the position we are in.
"A deal was in place when we brought Lee back which said Bristol City could call him back in January or we could keep him. It is something that will be sorted out next month. Paulo has to make his decision and then we will go from there."