The Reds enjoyed a successful first full campaign under Jurgen Klopp last season as the German coach led them to a fourth-placed finish in the Premier League.
Liverpool are now gearing up for a return to the Champions League next season as Klopp prepares for his second full campaign in charge at the Merseyside outfit.
The Reds looked like they were on course to challenge for the Premier League title last season before their form dipped off after the start of the new year and they were left to battle it out for a top-four finish.
Thompson feels that there are good times ahead for Liverpool and says that the Reds are capable of finishing third in the table next term.
Speaking to Sky Sports, Thompson said: “I think Liverpool will finish third.
“I would think we’ve got a good chance of winning a trophy, the FA Cup or the League Cup are well within our grasp, so as long as the team is progressing that would be a good return.
“This team hasn’t reached its potential yet and the key is to keep improving.”
Liverpool have brought in three new players so far this summer as the Reds prepare for the new season.
Klopp has signed Dominic Solanke, Mohamed Salah and Andy Robertson so far, although the Reds are continuing to be linked with a number of other players before the transfer window closes at the end of the month.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news