Parker has been keen to join a Premier League club following West Ham's relegation to the Championship and Spurs boss Harry Redknapp, a long-time admirer of the 30-year-old England international, seems to have won the race for his signature.
Allardyce told Sky Sports: "There are some negotiations going on and I don't think he would be mentally right to play. It will come to fruition in the next 24 hours or so."
Parker, who joined the Hammers from Newcastle for £7 million in 2007, was named Football Writers' Association Footballer of the Year last season even though his team finished bottom of the Premier League.
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