Sigurdsson is yet to sign a contract with the Swans despite agreement on a club-record £6.8million deal to sign him permanently from Hoffenheim following a successful loan spell.
Rodgers had pushed the Welsh club to sign Sigurdsson, who he also worked with at Reading, but the Northern Irishman's move to Anfield could prompt a rethink by the player.
Rodgers has vowed to let Sigurdsson talk to the new Swansea boss first - after agreeing with chairman Huw Jenkins not to poach any of his former players for 12 months - but said he would make a move for the Iceland international should any talks break down.
"Gylfi came to Swansea because I was there as manager and his scoring record was fantastic," he told various Sunday newspapers.
"I pushed the club to make an agreement [to sign Sigurdsson permanently] and they did that in terms of the fee - and agreed the salary. So I have said to Huw: 'I'm not going to do anything untoward. This is a guy you want, but it is down to Gylfi'.
"If he comes on the market I have to be interested. He knows that I rate his qualities and abilities.
"I said to Huw: 'If I speak to the kid I'll tell him to speak to the new manager, whoever that is'. But if he's not comfortable with that, he's in the market place then - and I have to look at him."
One of the top soccer cleats for control the Nike CTR360 will not let you down on the field in tight spaces.
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