Diame has impressed since joining West Ham on a three-year contract from Wigan Athletic in the summer, although he does have a release clause in his deal.
The 25-year-old's performances have seen Arsenal linked with a bid and reports in Sunday's papers claimed West Ham are ready to offer Diame a 'double-your-money' contract to scare off interest.
But Allardyce is confident that Diame, who is facing a few weeks on the sidelines after picking up a hamstring injury against Liverpool last weekend, will stay at Upton Park.
"He won't go anywhere," Allardyce told the Sunday Times. "He likes it here.
"[His improvement] is down to the challenge he's taken on. The size of a club demands a certain size of performance and we're a sell-out club, with 35,000 people, great tradition. He's responded.
"We changed his role. The ability he has to break through the opposition's midfield is rare. Other players have to pass their way through.
"He has similar capabilities to Yaya Toure though, unbelievably, Manchester City don't seem to be using those capabilities at the moment.
"That's why West Ham fans love him, those long, penetrating, weavey runs. He gets into the positions so often that if we can work on the finishing and final pass we could be talking about a really top player."
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