Having signed the 22-year-old Icelandic international on loan in January whilst in charge at the Liberty Stadium and a club record £6.8million deal for the player was agreed last month.
But the 39-year-old’s switch to Anfield has thrown a spanner into the works with many tipping Sigurdsson to follow him to Merseyside after confessing it’s unlikely he will sign for the Swans.
Rodgers has refused to get drawn into speculation and insisted the South Wales club should be given a chance to persuade the Hoffenheim star to stay at the club.
“First and foremost, Gylfi is a Hoffenheim player,” he told Liverpool’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.
“I wanted to sign him for Swansea but, like I’ve said to him and his representatives, that has to be his first port of call.
“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 has already reportedly drawn up his summer shopping list as he looks to improve the Liverpool squad but will continue to keep his cards close to his chest for now.
“I like to very much keep my counsel on potential targets,” he said. “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.
“I know what we’ve got, more or less, in the squad, but I also know there are a couple of signings that could really improve what we do.
“That’s something we’ll work together on over the course of the summer and hopefully we can get one or two in.”