Liverpool chief executive Ian Ayre has confirmed the club have already held talks with Steven Gerrard and his agent about the possibility of the captain making a surprise return to Merseyside on loan in the summer once he moves to Los Angeles Galaxy.
The club confirmed earlier in January that the legendary midfielder will put an end to his 17-year career at Anfield in the summer once his contract at the club expired.
The 34-year-old, who confirmed he will move to the US to play in the MLS, revealed he would have signed a new contract had it been offered before the start of the current season.
Meanwhile, asked about the captain's departure, Rodgers added: "Everything has been said on that situation that needs to be said.
"No doubt Steve is a world-class talent but the club has to keep moving forward. There's an opportunity for others to grab that mantra."
But now Ayre has claimed Liverpool are trying to convince him to return to the club on loan.
"The fact that he's leaving at the end of the season doesn't mean it's the last we'll see of him at Liverpool," he said, according to ITV.
"I've said openly to Steven and his representatives, as have Brendan and the owners, that we see Steven as part of the family."
Thierry Henry returned to Arsenal on loan during his time in the MLS, proving Gerrard could potentially do the same if he and his representatives decide it is a viable option.
Ayre said: "It's conceivable. It happens a lot in MLS and it's something we talked to Steven and his representatives about.
"What that means, the details aren't known yet, but we will keep a regular dialogue with him and I hope we will see him here again in the long term."