Francesco Guidolin accepts he could lose his job as Swansea manager if his side fail to beat Liverpool on Saturday.
Guidolin has come under increasing pressure with Swansea only one place above the relegation zone after failing to win a Premier League game since the opening day of the season.
Ryan Giggs - recently of Manchester United - and former United States boss Bob Bradley have been linked with the Liberty post, with the visit of Liverpool understood to be critical to the Italian's future.
Asked if he could be out of a job if Swansea fail to beat high-flying Liverpool, Guidolin replied: "It could happen. Maybe.
"It's not easy (to beat Liverpool). But if we win on Saturday for the period of the international break you don't speak any more about my position.
"But my position is not important, Swansea's (league) position is important, and we must get a result."
Swansea winger Nathan Dyer is likely to be sidelined until at least mid-November after undergoing ankle surgery.
Dyer, 28, had a successful operation this week to remove extra bone that had grown on his ankle.
"The operation went well," Swansea's head of performance Richard Buchanan told the club's official website.
"The specialists are pleased with the outcome, and it is estimated that Nathan is likely to be out for between seven and nine weeks."
Dyer has made two appearances this season after being on loan at Premier League champions Leicester last term.
He agreed a new four-year Swansea contract in August.
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Swansea forward Andre Ayew says his future depends on a summer discussion with club chairman Huw Jenkins.
Ayew was heavily linked with Sunderland during the January transfer window and there have been reports of summer interest from West Ham.
The Ghana international says he is happy at Swansea after finishing as the club's top-scorer this term with 12 goals.
But Ayew stopped short of committing himself to a second season in south Wales after scoring in Swansea's closing Premier League game, the 1-1 home draw with Manchester City on Sunday.
And, if the result of his talks with the club is a departure from Swansea, Ayew has made it clear he wishes to remain in the English top flight.
I'm happy here. If I have to stay, fine. If I have to leave, I have to leave. What is important for me is that I keep doing my work, and in football the truth of today is not the truth of tomorrow.
We'll see what's going to happen, we'll have a discussion and see the way forward. I've enjoyed the Premier League, I think it's the best league in the world. The intensity, the determination from every team. It's a league where you enjoy every game.
Every game is difficult, you can never say you've won it before you've played it. I hope to stay in the Premier League if I leave, but I'm here at the moment at Swansea.
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Swansea's press conference has been attended by first-team coach Alan Curtis and the club have confirmed that head coach Francesco Guidolin will miss Saturday's Premier League fixture against Norwich at the Liberty Stadium.
Guidolin has been in hospital with a chest infection since Wednesday that meant he missed the midweek win over Arsenal.
"He remains in a comfortable position and is making good progress, but doctors have advised that he misses this weekend's game to continue his recovery," read a statement on the club's website.
"He is expected to remain in hospital over the weekend before his release. Everyone at Swansea City continue to wish him a speedy recovery."
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