The Barclays Premier League new boys are hoping to strike a deal with the Reds over the England midfielder, who has failed to impress since joining from Chelsea last summer.
Liverpool could be ready to pick up a third of Cole's wage packet while he plays for the Loftus Road outfit, according to talkSPORT.
Chance to shine: Joe Cole in pre-season action against Malaysia last month
QPR face competition from Cole's former club West Ham, who are also interested in bringing him back to Upton Park on a season-long loan as they chase promotion back to the top flight at the first attempt.
Cole has found himself on the periphery of the team in an injury-hit first season at Liverpool, and Kenny Dalglish's arrival in January only served to push him further into the margins.
Old boy: Cole is wanted by former club West Ham
The 29-year-old playmaker hasfeatured heavily during the club's pre-season matches, but did not do his chances any good with an anonymous display in the embarrassing 3-0 loss to Hull on July 23.
But Dalglish's assistant Steve Clarke last month appeared to offer Cole a lifeline, suggesting he would get another chance to convince the Reds hierarchy that his future belongs at the club.
'At the end of last season he (Cole) was not getting in the team because the team was playing well,' said Clarke. 'But he has trained hard and gone away and had a good summer.
'Joe Cole is a top international player. He has got a big contribution to make to the future. He is the same Joe Cole I coached at Chelsea, just a couple of years older and a little wiser. He has always had this same fantastic attitude.
'He knows the position he is in. It has been difficult for him because he has not been involved but, when he gets the chance, it is up to him to take it.'
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