Remy has started both of the R's Premier League games so far this season and is a large part of Harry Redknapp's plans for the season, despite ongoing links suggesting the player will leave before the end of the transfer window.
QPR have now reportedly offered the 27-year-old a new contract at the club as they hope to hold on to the French forward whose projected move to Liverpool fell through last month because of a failed medical.
Remy will not sign any new deal until next Tuesday when the transfer window has closed because the pacey striker is still holding out on a big move away.
Chelsea may make an approach before the end of the deadline on Monday evening as Fernando Torres is believed to be close to sealing a switch to AC Milan, while Diego Costa has picked up a hamstring injury and is set to miss a number of games as a result.
Arsenal are also in a position where they should invest in a forward as Olivier Giroud will be out of action for three months with an ankle injury and Arsene Wenger may see Remy as an ideal acquisition to play as the lone striker during Giroud's absence.
Redknapp will be hoping that no offers are made for Remy, as the player's head will surely be turned when the likes of Chelsea or Arsenal come calling, but if no offers are made he could be set for a long-term stay at Loftus Road.