QPR boss Harry Redknapp has aired his optimism regarding a deal for the England international, with an agreement to bring the 32-year-old to Loftus Road believed to be close.
It is understood that he is poised to undergo a medical with the Championship promotion hopefuls, which would leave him on the verge of a summer switch.
QPR are, however, aware that they are not the only side to have expressed an interest in Parker's services.
Fulham are the latest club said to be readying an approach for a proven top flight performer.
Were the Cottagers to make a move, QPR assistant manager Kevin Bond acknowledges that it would be difficult to compete with a Premier League suitor.
He said in the Evening Standard: "If a Premier League club came in for him, that is the holy grail for players, so it will be difficult."