Rangers are said to be interested in bringing Morrison to Loftus Road on a temporary basis but Allardyce is just concentrating on getting the 21-year-old back to full fitness.
Morrison has been struggling with a groin complaint since December and has only been on the fringes of the Hammers' first team in recent weeks after making an impressive start to the season.
"At the moment, Rav is still complaining about the problem that he had before Christmas to say he has got these rumbling groin problems," said Allardyce.
"At the end of the day, he is going to have to decide if he goes for the hernia operation or not, and the answer keeps being no - he doesn't need it.
"What we have got to do is get him back training and back in the squad. I haven't heard any rumours any other way in terms of what is happening with Rav."
With captain Kevin Nolan scoring four goals in his last two games, coupled with the loan signing of Italy international Antonio Nocerino, Allardyce conceded former Manchester United youngster Morrison faces a battle to get back into the first-team picture.
"He certainly needs to get back and train with the squad," he added.
"He has to realise now everybody is fit there is severe competition here, especially with the new players as well.
"That severe competition brings pressure on the players that are playing in the first team, knowing that if they perform poorly they could lose their place, which is certainly the case at the moment with the size of the squad - which is good and healthy."