Listen to Ian Rush on talkSPORT
The Reds finished 25-points behind Pep Guardiola’s league winners in fourth last time out, but managed to reach the Champions League final.
When asked whether Liverpool can win the league next year, Rush told talkSPORT: “‘Why not?
“If you look at last season, I think there’s something to build on, they did really well and were great to watch.
“We weren’t expecting to get to the Champions League final, we got there and we’ve got to move forward now.
“Moving forward, realistically, is challenging Manchester City for the league. We beat them three times last year.”
The Reds have already secured the services of Naby Keita for next season and recently added Monaco’s Fabinho to their midfield. Lyon’s Nabil Fekir also looks set to join in the coming days.
But Rush, who won the league five times and remains the Reds’ all-time leading goalscorer with 346 goals, believes the club still need to sign another few players.
He continued: “We need three or four players in, but if we get that, I think we can genuinely challenge Manchester City.”