Lukaku has been in stunning form for Everton this season.
The Belgium international has netted 21 goals from 28 Premier League appearances.
He is the leading scorer in the top flight – two ahead of Tottenham star Harry Kane.
Romelu Lukaku not impressed at Everton training ground
Wed, March 15, 2017
Click through the gallery to see Romelu Lukaku's day at the Everton training ground
Everton FC via Getty Images
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Click to reveal snaps of Romelu Lukaku's day at the Everton training ground
Everton star Romelu Lukaku is wanted by Manchester United and Chelsea
Romelu Lukaku is currently on international duty with Belgium
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And Cottee reckons Everton should do whatever they can to stop Lukaku from leaving for the Premier League elite.
"The Lukaku situation is frustrating. If you're an Everton fan, you want it to be sorted out,” Cottee told Premier League Daily.
"You don't want to be reading that your top striker is 99 per cent certain of signing a contract and then, all of a sudden, he is not going to sign.
"I think only that man himself, Lukaku, knows the answer to it.
Romelu Lukaku has scored 21 goals for Everton this season
"The one thing you can't deny is he is still only 23 years of age, he has been in outstanding form this season, and he is one of the top strikers in Europe.
"Some people would say, if he doesn't want to be there, you cash in and you get the money.
"But, you try replacing him. Get your £50m, £60m, and try finding a striker that is going to fit that criteria.
"If it is about money, give him whatever he wants. Even if it is £250,000 a week.
"If you keep that player and he scores the goals that get you in the Champions League, it is an absolute bargain."