The England international is set to be formally released by the Premier League champions in the coming weeks, and is known to be on the lookout for a new club.
West Ham – who tried to sign him in January – were rumoured to be in pole position, but discussions recently broke down over the centre-back’s wage demands.
That has put the Super Hoops in contention, with Harry Redknapp thought to be committed to getting in experienced top tier performers following their play-off final win last weekend.
Lescott is seen a good option due to his lack of a transfer fee, and he could well jump at the wages on offer at Loftus Road – the club reportedly pay more in terms of salaries to players than Champions League runners-up Atletico Madrid.
QPR will also look to push through a permanent move for Wolves’ Kevin Doyle.
The Republic of Ireland international joined the R’s on loan in January, firing two goals in 11 outings to help the Londoners to promotion.
Despite the midlands club’s rise to the Championship from League One, they are rumoured to want the former Reading star’s wages off of their expenditure.