The England international was expected to be snapped up quickly this summer after the Hammers' relegation from the Barclays Premier League with Aston Villa and Chelsea both linked with the player.
But Allardyce insists West Ham have received no bids and it now looks increasingly likely that Parker, who was so impressive last season, will start Sunday's Championship opener against Cardiff.
No offers: But West Ham are planning for life without star midfielder Scott Parker
Although the former Bolton boss admits he is planning for life without the 30-year-old as he expects that a Premier League club may come in for him once the season has started.
Allardyce claims Parker is desperate to play in the top-flight and could still leave before the summer transfer window slams shut on August 31.
'I'm planning for life with and without Scott Parker,' said Allardyce. 'If the right club comes with the right money then we are going to release Scott because he wants to play in the Premier League. We do need the finances that will bring.'
Snub: Carlton Cole decided against a move to Stoke City and remains a Hammer
Allardyce did reveal that West Ham had received bids for striker Carlton Cole, who has turned down a move to Stoke, and goalkeeper Robert Green. He described the offer for Green from West Bromwich as an 'insult'.
'We've only received a bid for Carlton Cole that was good enough for us to accept. We had an insult of a bid from West Brom for Robert Green and that was rejected straight away, but we haven't had any bid at all for Scott Parker at the moment.
'But that can all change when we get into August because people pick up injuries, they start to wonder whether they've got what they really need, the mayhem will continue until the end of August.'
Nolan determined to win promotion at first attempt with West Ham Time running out for Parker deal, West Ham boss Allardyce tells Spurs