Sturridge has been plagued by injury and poor form this campaign and has scored just two Premier League goals for the Reds.
He’s looked a far cry from the player that scored 21 goals in the top flight during the 2013-14 season, the Liverpool Echo report.
The England striker has two years left to run on his current contract at Anfield and club legend John Barnes wants him to see them out – despite continual speculation that he could leave in the summer.
French champions PSG were reported to be interested in signing him on loan in January, while West Ham are said to be keen on taking him to London.
Liverpool boss Jurgen Klopp has admitted that talks over the England international’s future will be put on hold until the end of the season.
But speaking to HITC Sport, Barnes insisted that now would be the wrong time for Sturridge to move on and would like to see him stay with the Reds.
He said: “Well, I would like to think that he should stick around.
“How is he going to move? First of all, someone has to make an offer for him, someone has to sign him and pay his salary.”
Steven Gerrard: Liverpool need Daniel Sturridge
Barnes added: “Daniel Sturridge is a fantastic player.
“What I would like to see is a fit and motivated Daniel Sturridge, and in those circumstances, of course I would like to see him stay.”
Sturridge has not featured for Liverpool since February 4, due to a combination of illness and injury.
Yet to return to full training, he is likely to miss Sunday’s trip to former club Manchester City.