The England trio are expected to leave the Hammers this summer following their relegation to the Championship.
Allardyce accepts that some of his squad will want to be playing top-flight football next season, but insists no offers have been forthcoming as yet.
Parker has been linked with Tottenham, Cole with Stoke and Green with Aston Villa.
"The speculation is around Rob Green, Carlton Cole and Scott Parker, and at the moment we haven't had any concrete bids for those players," he said.
"Other than that there is no rush to sell anyone else.
"We will probably look at moving some of the players on because their desire is to play in Premier League.
"From a financial point of view, it suits us to lose that financial commitment because the drastic loss in revenue [following relegation] is what we all have to face at West Ham; certainly the owners, who've got to really back up with their own money to help us try to get back in the Premier League.
"We will try and get as good a squad as we can. There's some very good players at the club. If we all want to work together and go in the right direction, we can give it our best shot and hopefully that will be enough next season."
Allardyce has yet to speak to any senior players at the club and admitted there was still much to be done.
"Before we all get together I've got an awful lot to sort out in terms of pre-season training, staffing, relocation for myself, so I'm going to try and do that before the players get back and then speak to them on an individual and group basis," he said.
Allardyce also bristled at the suggestion that he needed to win over the Hammers fans by playing attractive football - the so-called 'West Ham way'.
"When did West Ham play the West Ham way?" he said.
"It can't be the West Ham way if you get relegated, and the club's been up and down like a yo-yo [in recent years].
"I don't think the fans see that as playing the West Ham way.
"The West Ham way is about winning football matches and the enjoyment of winning.
"The fans are in the game to watch winning football, I'm in the game to play winning football and entertain the public, and that's what I do.
"Everywhere I've been I entertain the public, irrespective of the perception from the media that Sam Allardyce plays long ball.
"That is only a perception, but most of football is run on perception today."