The 21-year-old midfielder, a former Manchester United trainee, left for Championship club Queens Park Rangers on a 93-day loan earlier this week having not started a Premier League match since December.
Media reports said Morrison was unhappy about pressure from Allardyce to sign up with his agent Mark Curtis, a suggestion the 59-year-old rejected.
"It's completely unfounded," Allardyce told reporters ahead of mid-table West Ham's home league game with Southampton on Saturday. "The rumours or allegations will be made probably by Ravel's representatives.
"There's no truth in the fact I have sat with Ravel Morrison and tried to press him into signing anything with any agent, never mind mine. It's his choice and his decision, not mine - unless they ask me."
Morrison made a stunning start to the season that had some observers touting him for an England call-up.
Allardyce would not answer questions about why he let Morrison leave but said he still had a future at the club when his loan spell ended.
"Ravel wanted to play some first-team football. He wasn't getting it as much here as he wanted so we've let him go on loan," said the West Ham boss.
"Our consistent performances and the acquisitions of (Antonio) Nocerino, (Marco) Borriello and (Pablo) Armero have given us a bigger squad and Ravel has found it a little more difficult to get in."
(Reporting by Josh Reich; editing by Tony Jimenez)
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