The striker has been linked with Juventus, Real Madrid and PSG among others.
The Belgian has enjoyed a fine campaign for the Blues, scoring 25 goals in all competitions so far.
18 of those have come in the Premier League as he competes with Harry Kane and Jamie Vardy for the Golden Boot.
His performances have not gone unnoticed, with a number of Europe’s elite clubs thought to be keeping track of his progress.
The international break has seen rumours of an exit intensify, fuelled by comments from Lukaku himself, but Martinez insists that his ambition is a positive.
"It's not unsettling because that should be the aspirations of everyone. Being the best you can,” he told the Liverpool Echo.
"That's our aspiration - to be in the Champions League. I've said it openly for a long time. We want to be competing to win titles.”
"Now we're in the semi-final of the FA Cup. The players need to be part of that and we need ambitious players who can carry the expectations of our football club."
Lukaku’s future certainly seems like it will be under intense focus once the summer transfer window rolls around.
There is no denying that the Blues have failed to match his ambition, with them currently sitting 12th in the table after another hugely disappointing campaign.
With a place in the FA Cup final up for grabs though, winning that tournament could be their last hope of convincing the striker to stay beyond this year.