The England forward’s Liverpool career has been blighted by injury since he arrived at the Merseyside outfit from Chelsea in January 2013.
Sturridge has made just 60 Premier League appearances for the Merseyside outfit since his arrival at Anfield three years ago and manager Jurgen Klopp admitted on Friday that he is unsure when the forward will be back available for selection.
The 26-year-old has only started three Premier League games for Liverpool so far this season, with his last appearance coming during the 2-0 loss to Newcastle United on 6 December.
And former Liverpool man Thompson feels that the Reds’ owners will be considering selling the forward in the near future if he is unable to prove his fitness on a regular basis.
Thompson told the Daily Mirror: “There’s only so far you can go with Sturridge.
“You can’t build a team around him. You can’t even build a forward line around him.
“It’s hard to envisage going forward with a player like that.
“I think they [the owners] will be looking at him, how many minutes he played, how old he is, wondering how much they can get for him.”
Liverpool travel to Leicester City in their next Premier League game on Tuesday night.
MORE: Latest Man Utd news
MORE: Latest Arsenal news
MORE: The latest football news