Lukaku joined Manchester United from Everton for a fee of £75million last Monday, signing a five-year contract at Old Trafford.
Jose Mourinho turned his attentions to the Belgian after growing frustrated at the length of time a deal for Real Madrid's Alvaro Morata was taking.
But Burley is not convinced Mourinho thinks Lukaku is the right man to replace the goals scored by the now departed Zlatan Ibrahimovic last season.
"The way I'm seeing it is, I'm not convinced that he (Mourinho) is convinced that Lukaku is the man to really do the job for him," Burley said on ESPN FC.
"But he was needing somebody and he was the one he could get for that kind of money. In terms of Lukaku being good enough, I'm not so sure.
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People will say 'Sergio Aguero, plays for Man City, he's not going to play for Man Utd'. Well Carlos Tevez did it
Craig Burley on Manchester City striker Sergio Aguero
"Let's look at it one way. United are trying to get back to the top of the perch, not just in England but in Europe.
"In that case you've got to go out and get the best. They did go out and get (Paul) Pogba but the striker position is so opponent.
"The best are in Spain, the best are in Germany with Bayern Munich, in fact he's not even the best in the Premier League."
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Burley says Aguero and Tottenham's back-to-back Golden Boot winner Harry Kane are the top two forwards in England.
Sergio Aguero would be a better option for Man Utd than Romelu Lukaku, says Craig Burley
And he says, despite the city rivalry, Aguero could have been an option for United, similar to how Carlos Tevez went in the opposite direction in 2009.
"If you take into account Sergio Aguero, who could be surplus to requirements at Man City, and Harry Kane," Burley added.
"People will say 'Sergio Aguero, plays for Man City, he's not going to play for Manchester Utd'. Well Carlos Tevez did it, he went from United to City, it has happened.
"What I'm saying is he didn't even get the best striker in my opinion in the Premier League.
"Good luck to the lad, he's a youngster, it's a great opportunity. But I tell you what, there's going to be no hiding place."