The 36-year-old made 710 appearances for the Reds after joining the club's Academy aged nine, but left in the summer of 2015 at the expiry of his contract.
Feeling he could still continue his playing days, he joined LA Galaxy and has been in the United States since - but injuries and poor form have limited him to 36 appearances and five goals in two Major League Soccer seasons.
Gerrard took to social media at the weekend to strongly suggest that he would be leaving the Galaxy, with the MLS season coming to a close next month, saying that it "has been a privilege" to play for the club.
Bruce Arena's side played their final game of the regular season against FC Dallas on Sunday, Gerrard uninvolved due to a hamstring injury, having already sealed their place in the MLS play-offs.
But Gerrard is expected to leave at the end of his contract in America and has had the way paved for him to make an emotional return to Anfield - though in a coaching capacity rather than as a player.
Klopp leaves the door open for Gerrard to return
In the aftermath of Liverpool's 2-1 win over West Bromwich Albion on Saturday, when asked about a potential Gerrard return, Klopp said that the Huyton-born midfielder would always be "so welcome" at the club.
"You cannot imagine how welcome," he told reporters, adding: "Everything which we have already or will speak to each about stays in this situation [between us]. But nobody should be worried that there is no space for Steven Gerrard. Everything will be fine. 100 per-cent."
Gerrard trained with Liverpool last November while between off MLS seasons and was back on Merseyside just last month to seek extra assessment on his current injury, despite having already had medical help from experts in Los Angeles.
While back in his homeland, he visited the club's Melwood training ground and it has since been revealed that he is in discussions with the club over a return which could see him take up a coaching role.
The sticking point, rather than being the level of his role, is likely to come in the fact that former England skipper Gerrard feels he can still prolong his career further.
He is currently taking his UEFA A Licence - just one level below the Pro Licence qualification required to manage in the Premier League and UEFA competitions - and has previously suggested that he has spoken personally with Klopp about the possibility of working with Liverpool.
He said, at that time, that no offer was on the table but that club had made it aware they were keen to see him come back - but it is now thought that Liverpool are looking to bring perhaps their best ever player back in to the fold within the coming months.