The former defender feels the failure to qualify for the Champions League will see the youngster leave.
The Reds drew with Chelsea 1-1 at Stamford Bridge on Sunday, a result that all but ended their hopes of finishing in the top four and qualifying for the Champions League.
And Thompson believes that will make it very hard for the 20-year-old to stay at Anfield with speculation about his future still ongoing due to his reluctance to sign a new contract at the club.
“I think it will be very difficult for him to stay at Liverpool now. He’s shown all the signs that he’s ready and prepared to leave the club,” he said.
Regardless of whether Sterling does leave or decides to stay, Thompson insists that the player has no future as a striker.
The youngster has been used as the focal point for the Liverpool attack this season in the absence of Daniel Sturridge, who has missed the majority of the campaign through injury.
Elsewhere, the likes of Mario Balotelli, Rickie Lambert and Fabio Borini have all failed to seize the opportunity to grab the striker role for themselves, forcing manager Brendan Rodgers to use Sterling as his lone forward.
Thompson though, insists that the player is best used out wide and the experiment as a striker must come to an end.
“No matter where he is next season, I think his best role is out wide rather than through the middle,” he added.
“He’s done well for the team – he’s helped them out up front this season, but I think everyone can see that he’s not quite strong enough for it. He’s not a natural goalscorer.”