The Iceland international has agreed terms with the Swans after a successful loan spell from parent club Hoffenheim last season, but Rodgers’ switch to the Reds has thrown the move into doubt.
And, while revealing his continued interest in the player, Rodgers has vowed not to deter the midfielder from joining his former side.
"I wanted to sign him [Sigurdsson] for Swansea but, like I've said to him and his representatives, that has to be his first port of call,” Rodgers told the club’s official website.
"I took him on loan for the second half of last season and he did very, very well. He scored seven goals and made a real, positive contribution.
"If he comes into the market for whatever reason - and I'm sure there'll be a number of clubs interested in Gylfi - then of course I would like to be in a position to put our case here at Liverpool to sign him.
"But I've always said, I think he's a player Swansea have had an agreement with and they have to have every chance to try and sign him. That's only right.
"If anything changes from that, we'll look at it from there."
Rodgers also revealed that he has outlined the other players he is interested in bringing to Liverpool, but is unwilling to disclose any names.
Chelsea's Salomon Kalou has been linked in recent weeks, with the Ivory Coast international's agent stating that his player would be interested in a move to Anfield.
"I like to very much keep my counsel on potential targets," he continued. "I think there are a few players who can come in and improve the group straight away.
"I know the types of player I need to bring here to make us function well and that's something myself, the club and the board will look at.
"The problem with a club like Liverpool is they get linked with every player going. That's the way of the world these days.
“Every player wants to play for Liverpool. The magnitude, the size and the history of the club, and the quality of the people here in the city, means people will want to come and play here.”