The 30-year-old was voted Player of the Year by the Football Writers' Association last season, despite being relegated to the Championship. He has since been linked with a return to the Premier League, with both Spurs and Chelsea reportedly interested.
However, the Hammers boss has insisted that the club will not agree to sell their star midfielder unless he is given time to reinvest that money – reported to be in the region of £4m - in his own side.
"It is a worry that Spurs might wait until the last minute," Allardyce told reporters.
"So if Harry [Redknapp] is listening, or anyone at Tottenham, watch out, don't be waiting that long because you won't be able to do it."
Parker joined West Ham from Newcastle in 2007 and has made 109 appearances for the club.