Controversial midfielder Morrison was loaned to Rangers by Allardyce in February after dropping out of favour despite some impressive early-season displays for the Hammers.
Reports this week claimed the 21-year-old does not want to return to Upton Park if Allardyce is still in charge next season.
But Morrison took to Twitter to scotch the rumours, saying: "Papers talk a lot of rubbish I don't care what manager I play under all I want to do is play football #WHU."
Morrison has scored six goals in 15 appearances for Rangers and was named Championship Player of the Month for March.
Under the terms of his loan deal he is available for the forthcoming play-offs as Harry Redknapp's men attempt to secure promotion back to the Premier League.