The Red Devils spent £75 million on the Belgium international over the summer having found themselves short of a leading frontman.
Ibrahimovic had been released at the end of an initial 12-month stint at Old Trafford, with the Swede nursing knee ligament damage which had brought his campaign to a close.
He has since been drafted back in on another short-term deal and Parker believes his vast experience – and Lukaku’s lack of at the very highest level – will see Jose Mourinho favour a 35-year-old striker in Europe once in a position to make such a selection choice.
The former United defender wrote in a column for Eurosport: “There’s a few players in that United squad who have very little experience at this kind of level, particularly in the attack: Lukaku, Marcus Rashford and Anthony Martial spring to mind.
“Lukaku worries me a bit as the most important thing in Champions League football is ball retention and to kill the game, especially if you get a goal in front. Patience is vital. He doesn’t strike me as that kind of player – at least at the moment.
“It’s a very different task to playing in the Premier League where he is undoubtedly one of the best strikers of the past five years.
“That’s why I think Zlatan could play a bigger role in Europe than he does in the Premier League this season.
“If he comes back in November, December or January – whenever it may be – then when United start the knockouts in February, providing they make it, it will be Ibrahimovic who leads the line and Lukaku will be on the bench, without a shadow of a doubt.”
Lukaku will be hoping to put down an early marker and prove his Champions League credentials when United open their 2017-18 group stage campaign with a home date against Basel on Tuesday.
The 24-year-old has netted five times in as many competitive appearances this season to offer an immediate return on the sizeable investment made in his talent.