The England under-21 international has been the subject of speculation linking him with a move away from Upton Park in the close-season.
Morrison made a big impact at West Ham during the first half of the previous campaign, and scored a superb solo goal in a 3-0 win at Tottenham in October.
He was then loaned out to QPR in February, and helped Harry Redknapp's men gain promotion to the Premier League via the play-offs.
Speaking on Saturday, Allardyce revealed that the 21-year-old had struggled with a hernia problem, and was hopeful that surgery would help to bring the playmaker back to his best.
"He's contracted to West Ham," he said. "I think he's had a hernia op.
"Once that's healed up I hope he becomes a better player because he has been playing with it for a while. The groins have been causing him a problem for a while.
"If you've got pain I don't think you perform to your best. Hopefully that pain will have ended and he'll be a much freer, more active player for us. If he could do what he did last season that would be great because when he broke in to the side early last year he had a great spell. Unfortunately he couldn't sustain it.
"If he continues to do what he did last season then yes [we want to keep him]. But that does depend on how much players want. How much they demand. If that demand is far too great then that becomes a difficulty for us."