The Sunday Mirror says the 12-month agreement which prevents Kop boss Rodgers from signing Swansea players does not cover Sigurdsson, the Icelandic international who spent the final four months of the season on-loan from German club Hoffenheim.
And Rodgers made it clear that he is ready to pounce – even though Swansea believed they had a £6.8million agreement in place to sign the 22-year-old permanently.
He said: “When I had a chat with Huw Jenkins the other day, after I told him I was going to Liverpool, I gave him assurances that I wouldn’t be going back for any players. My word still stands on that. But Gylfi came to Swansea because I was the manager there.
“I actually pushed Swansea towards making an agreement with Gylfi – and they eventually did that in terms of the fee and then the salary. But ultimately it’s now down to Gylfi.
“I have told Huw that if I speak to the kid, I will make sure he definitely goes down to Swansea and speaks to the new manager, whoever that is.
“But if Gylfi is not comfortable with that and he comes back on to the market then I have to be interested.”