That is according to former Everton star and pundit Leon Osman, who believes Liverpool need to strengthen up-front this summer.
After a difficult start to the season, Vardy ended it with a bang, scoring 10 goals in his last 17 matches for Leicester.
Liverpool striker Daniel Sturridge once again struggled with injury and fitness problems, starting just three Premier League games in 2017.
The England man has been linked with an exit from Anfield with Klopp not being able to rely on the 27-year-old.
Leon Osman believes Jamie Vardy would be a good signing for Liverpool Liverpool transfers: Most likely summer deals Thu, April 20, 2017
Express Sport takes a look at the most likely summer signings Liverpool might secure according to the bookies. Odds provided by 888sport
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Who is Jurgen Klopp tipped to sign this summer?
I think someone like Jamie Vardy might work for Liverpool
Leon Osman on Leicester striker Jamie Vardy
Osman believes Vardy would fit into the pressing game Liverpool play under the former Borussia Dortmund manager.
"He does like the mobile striker," he said on BBC Radio 5 Live.
"I'm looking at who he can possibly go for.
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Leon Osman says Jamie Vardy would suit Jurgen Klopp's style of play at Liverpool
"He likes the mobile, he likes to be able to chase the ball down. But he's missing a centre-forward.
"I think someone like Jamie Vardy might work for Liverpool.
"He would chase round like the way they like to press and he also likes to play on the shoulders. He makes clever runs."