Last week the Swans agreed a £6.8 million transfer - almost doubling their record fee - to sign the player from Hoffenheim permanently after his successful four-month loan spell subject to a medical.
However, Rodgers' departure to Anfield cast doubt on the deal and Sigurdsson now does not think he will complete it - despite being keen to remain in the Premier League. He told mbl.is in his homeland: "It's just unclear at this moment where I will play."
He added: "I'd like to play on with Swansea since I was really happy there but after Brendan Rodgers left the club for Liverpool, that changed the situation.
"I expect not to stay at Swansea because of the uncertainty going on there as it is not clear who is boss.
"I have said that my desire to continue playing in the Premier League and Liverpool is completely considered.
"Liverpool is a big club that has a glorious history.
"English Premier League is the platform that I want to be and hopefully is that I continue to play in that division."
Sigurdsson has been in touch with Rodgers - a manager he rates highly - since he was installed as Kenny Dalglish's successor, which raises the prospect of him ending up at Anfield.
"I got in touch with Brendan when he was appointed Liverpool manager," he added. "I wish him congratulations and thanked him for a great time at Swansea."