Lukaku has had an outstanding campaign since joining the Baggies on loan from Chelsea.
The 19-year-old has scored 13 Premier League goals, at an average of just over one in every two games and given the opportunity, Clarke would love to have him back at The Hawthorns next season.
Yet the issue is complicated.
For with a new coach due to be installed at Stamford Bridge in the summer, it is not known whether Lukaku will be available.
In addition, there have been suggestions the lure of European football might be enough to lure Lukaku to Swansea, who qualified for the Europa League thanks to their Capital One Cup success over Bradford in February.
Evidently, it is not a theory Clarke is willing to go along with.
"There is nothing in it," said the Baggies chief.
"It is idle gossip - it's lazy.
"I read in the press he's going to Swansea - but I would be very surprised if he ends up there."
At the end of his first full season as a manager in his own right, Clarke faces the delicate task of attempting to strengthen a squad currently on course for an eighth-place finish, whilst warding off predators with bigger budgets, attracted by the results West Brom have achieved this season.
"We're not concerned about losing players," he said. "It's a compliment.
"It means we've had a good season.
"But if anyone comes for our players they will have to pay a lot of money."
West Brom have cemented their status as a top-flight club by adopting a prudent approach in the transfer market, whilst loosening the purse strings for one significant new arrival, which last summer was England goalkeeper Ben Foster.
The policy has clearly been a successful one. And, for Clarke, if nothing is broken, there is no need to fix it.
"I see no reason why the policy would change," he said.
"Over the recent seasons we've been successful and I imagine that's the model that will continue.
"I have a list of players myself and we will try to sift through them to get the best three, four or five players to complement what we have already got.
"But I would also like to think we could get one marquee signing.
"Last summer we got Ben. He was a big signing for us.
"This year we need to try to find someone else to do as good a job as he did in whichever position we make that signing in."