The Iceland international impressed while on loan at Rodgers’ former club Swansea last season.
Sigurdsson has agreed terms with Swansea, but the midfielder could yet end up at Anfield next season.
“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.”
