The Reds captain will end his 25-year-long association with the club this summer when he departs for a new challenge in Major League Soccer.
Principal owner John Henry and manager Brendan Rodgers have said there will always be a role for the midfielder at the club whenever he decides to return from America.
Chief executive Ian Ayre says that could be as soon as next winter during the MLS off-season.
“I’ve said openly to Steven and his representatives, as have Brendan and the owners, that we see Steven as part of the family,” he told Liverpool radio station CityTalk.
“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.
“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.”
Asked if that could mean a return on loan next January, Ayre said: “It’s conceivable. It happens a lot in MLS, and it’s something we talked to Steven and his representatives about.
“You can’t have someone who has so much of the club’s DNA in them and just expect that it will go away.”
Ayre insisted the timing of a “substantial” contract offer would not have made a difference to Gerrard’s decision despite the player claiming he probably would have signed a new deal in the summer.
“Let’s assume that we’d made that offer (in the summer) and that he’d signed it. I think we’d still be in the same position today,” he added.
“Just like any player, at any club, if he all of a sudden isn’t playing every week, they maybe start to think ‘Maybe this isn’t the place for me now’.
“Steven may have signed that contract but we may have been sat round now in the same position.??We’ve had that before with very senior players. I had one come to me and say ‘I don’t really fancy this any more’.
“Who knows how it would have played out? But I think Steven made the point last week that it (not playing every week) doesn’t appeal to him.
“So the fact that he would have signed a contract last season actually doesn’t make any difference.??His point was that after playing every week, playing a bit-part role is not how he wanted to finish his career.??He wants to finish on a high and I am sure he will.”