Sigurdsson has verbally agreed a club record £6.8m move from Hoffenheim to the Swans but has yet to sign.
The attacking midfielder played under Rodgers at their former club Reading and the Reds boss said: "If he comes on the market I have to be interested.
"He knows that I rate his qualities and abilities."
Swansea's agreement for Rodgers to move to Anfield included a clause preventing Liverpool bidding for any Swansea players within 12 months.
But Rodgers says Sigurdsson, 22, joined on loan from German club Hoffenheim in January only because the Northern Irishman was in charge.
"Gylfi came to Swansea because I was there as manager and his scoring record was fantastic," said Rodgers.
"I pushed the club to make an agreement to sign Sigurdsson permanently and they did that in terms of the fee - and agreed the salary.
"So I have said to Huw [Jenkins, Swansea chairman]: 'I'm not going to do anything untoward. This is a guy you want, but it is down to Gylfi'.
"If he comes on the market I have to be interested. He knows that I rate his qualities and abilities.
"I said to Huw: 'If I speak to the kid, I'll tell him to speak to the new manager, whoever that is'.
"But if he's not comfortable with that, he's in the market place then - and I have to look at him."
The 22-year-old impressed during his spell at the Liberty Stadium and scored seven goals in 17 starts.
Hoffenheim signed Sigurdsson in 2010 for £6.5m from Reading.
Swansea's initial bid, thought to be close to £4m, was rejected by the Bundesliga club, who are keen to recoup the fee they paid for Sigurdsson.
The Welsh club earned £45.9m from television and prize money during their first season in the Premier League, finishing 11th in the table, and so have funds to strengthen the squad.
Sigurdsson said in April he would be happy to stay at the Liberty Stadium beyond the end of the season.
But Swansea chairman Huw Jenkins had also admitted the Welsh club would struggle to keep hold of the midfielder.