Despite the Hammers finishing bottom of the Premier League last term, the England international was named Football Writers' Player of the Year for the campaign, and several sides are said to be keen on signing the 30-year-old from the relegated East London side.
Aston Villa, Arsenal, Tottenham Hotspur and former club Chelsea have all been linked with the Irons' skipper in recent weeks, but no club has yet tabled a bid deemed acceptable by West Ham.
However, the newly-appointed Hammers boss has revealed he is reluctant to build his plans around the former Charlton Athletic and Newcastle United star in the fear he will leave the club before the transfer window closes at the end of the month.
"At the end of the day, Scott's position is delicate because at any one time, someone will hit the numbers that we would value him at," Allardyce said, as reported by The Sun.
"If that's the case and it's the Premier League - a place where he wants to be - he will be gone. It would be wrong of me to plan with Scott."
West Ham start their Championship campaign with a home game against Cardiff City on Sunday.
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