Relegated West Ham are keen to get the England striker off the wage bill as they prepare for life in The Championship and will listen to bids of around ?6 million.
Stoke had a ?3m bid for Cole rejected by West Ham earlier in the summer, and have not returned with an improved bid.
Wanted man: Carlton Cole could be offered a chance to remain in the Premier League with QPR
The 27-year-old striker has two years remaining on his contract at Upton Park and his departure could pave the way for Blackpool striker DJ Campbell to join the Hammers.
Sam Allardyce has been chasing Campbell for the last month and triggered the ?1.25m release clause in his contract, but the striker is keen to move to a Premier League club.
Hammer time: Sam Allardyce is keen to bring Blackpool striker DJ Campbell to West Ham
If QPR are successful with a move for Cole, Warnock admitted that it is unlikely that the striker will partner Adel Taarabt, as the Moroccan international looks set to leave the Premier League new boys.
Warnock said: 'PSG [Paris St-Germain] have made an inquiry and they obviously offer him the chance to be nearer to home, although there is a Spanish club being mentioned as well.
'As far as his talk of wanting to go to Chelsea or Arsenal, I know he has a lot of friends at Arsenal. He is missing his family in Marseille.
Uncertain future: Neil Warnock believes that Adel Taarabt could leave QPR this summer
'If we get a big offer from a club in France that obviously gives him a chance to be closer to them. That would be a big pull.
'Flavio Briatore [the QPR co-owner] is dealing with the negotiations. He is keeping me informed of the situation and at this precise moment [Adel] won't be leaving because no one has met the asking price.'
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