The Canada international has been tipped to make an exit from the Stade Pierre-Mauroy for a couple of seasons now, and he is now in the last year of his contract with the 2020-21 French champions.
With Lille running the risk of losing David for nothing in 2025, it was said that a fee of around £25m could have been enough to prise him away from Les Dogues in the summer transfer window.
Tottenham Hotspur, Manchester United, Chelsea and West Ham United were heavily linked with a move for David over the summer, but the Premier League window slammed shut with the striker still at Lille.
There is still the possibility that David could join a club in Greece or Turkey over the next few days if Lille are desperate to get rid of him, but he will seemingly remain in France until January at the earliest.
David confirms talks over new Lille contract
Opening up on the summer saga to The Athletic, David revealed that he was in talks with a couple of teams, and he is not putting all of his eggs in the Premier League basket.
The Canadian also confirmed that he is discussing a possible contract extension with Les Dogues, which would allow them to recoup a fee next summer rather than lose the prolific striker on a free.
"I spoke to a couple of teams. I spoke with coaches. But ultimately (David and his camp) made the decision to stay," the 24-year-old said. "What am I waiting for? I guess now it's easier to say.
"I'm in the last year of my contract. Eventually my contract is going to run out. So then we'll see. We'll see what happens next year. Right now we're speaking with the (Lille President Olivier Letang) about a possible extension. We'll see how that goes.
David "open to anything" amid Premier League links
"I'm open to anything. I think obviously the Premier League is regarded as one of the best league in the world. And for me it's not the Premier League or bust. I'm open to anything and every league has its challenges."
Lille signed David from Belgian side Genk for €28m (£22.8m) in the summer of 2020, and the attacker won the Ligue 1 title in his first season with the club, scoring 13 goals as part of an effective strike partnership with Burak Yilmaz.
The Canada international has now amassed a total of 87 goals and 20 assists in 190 matches for Les Dogues, netting three strikes of his own and setting up two more in seven fixtures already this term.
With David and his camp unable to reach agreements with any interested party, all rumoured Premier League suitors moved on, as Tottenham Hotspur smashed their transfer record on the £65m signing of Dominic Solanke from Bournemouth.
Meanwhile, Man United and West Ham captured Joshua Zirkzee and Niclas Fullkrug respectively, while Chelsea did not bring in a new senior number nine in the summer transfer window.