The Icelandic playmaker was all set to complete a permanent move to Swansea from Hoffenheim this week before Rodgers quit for Liverpool.
But his exit has thrown Sigurdsson's future into doubt, and Rodgers admits he would be keen to bring the 22-year-old on board at Liverpool as he plots to make them Premier League challengers.
"If he [Sigurdsson] comes onto the market, I have to be interested," said Rodgers. “His initial chat has to be with Swansea, because he had a good period there.
"I said when I had the chat with the chairman (Huw Jenkins) the other day, when I told him I was going to go to Liverpool, that Gylfi came to Swansea because I was there as manager.
"I said to Huw if I speak to the kid I'll tell him to make sure he certainly comes down and speaks to the new (Swansea) manager, whoever that is, and that if he's still not comfortable with that, he's in the marketplace then - and then I have to look at him."