Allardyce is planning without the England Under-21 midfielder ahead of the new season, but co-owner David Sullivan has confirmed the board to not want to sell him.
Morrison fell out of favour last season and was shipped out on loan to QPR, where he helped Harry Redknapp’s men win promotion back to the Premier League.
Swansea and CSKA Moscow have been linked with the former Manchester United star, but Sullivan insists he wants to see Morrison stay at Upton Park.
"Sam has said Ravel is not part of his plans but we do - as a board - see him as part of our plans," Sullivan told talkSPORT.
"I think he (Allardyce) said in a press conference, if I read it correctly, he's not part of his plans for this season. I think he said that in New Zealand but we don't agree with that. We would like to sit down and give him a longer contract."
Sullivan added: "We do like him. We do see him as part of the long-term future of the club but we have to agree it with the manager because there's no point signing a player he's not going to play."
Morrison, 21, was left at home as the remainder of the West Ham squad jetted off for a pre-season tour of New Zealand, with the club confirming he underwent successful groin surgery.
Having spent time at St George's Park since his operation, Morrison should be fit and ready to rejoin the first-team squad when they return from their trip.