Morrison, 21, made an impressive start to the season after signing from Manchester United, but his form has since waned, prompting media reports he is to join second-tier Queens Park Rangers on loan.
Although Allardyce refused to answer questions about Morrison’s future at the club, he did express annoyance at his reluctance to play through the pain of his injury.
“Listening to our medical staff, there’s no problem that he can carry on – not at all,” Allardyce said.
“He says he feels it occasionally. Instead of gritting your teeth and getting on with it… he’s not the type.
“Lots and lots of players throughout the country will be playing with a similar type of injury the medical team say, ‘You can carry on, it’s not a problem.’”
QPR manager Harry Redknapp has confirmed his interest in signing Morrison.
Speaking after his side’s 1-0 loss at Derby County yesterday, he told Sky Sports News: “It’s a possibility. I’ve been trying to ring Sam all day. I think he’d like to come and if Sam wants to loan him, we’re here.”