Lukaku’s future at Goodison Park is now in serious doubt, with the striker stalling over accepting a new contract.
The Belgian international’s current deal expires at the end of next season, meaning Everton may be forced to cash in during the summer - unless he accepts their terms.
A host of clubs are said to be interested in Lukaku, and Redknapp feels that the 23-year-old is ready to step up.
“I do feel Lukaku is ready to move on and test himself at a bigger club,” Redknapp said. “While I am not sure where he would go, Lukaku could be the perfect player to replace Diego Costa should he leave Chelsea in the summer.
“But it is one thing to score two goals at the end of a game against 10-man, relegation-threatened Hull and another to do it against the top teams.
“That is the key difference between Costa and Lukaku — Costa affects the big matches. Should Lukaku return to Chelsea, that is what he would need to bring to his game.”
Lukaku scored twice for Everton in his most recent appearance against Hull City, as he continued his fine form.
Lukaku now leads the Premier League’s scoring charts, with 21 goals to his name for the season.
Everton are still desperate to keep hold of Lukaku, and their league finish may be crucial to holding on to their star striker.
Everton’s win over Hull has lifted them into the battle for a European place, and they have now drawn level on points with Arsenal.