"Why me and not Moyes?" asks Allardyce
Speculation has continued to grow about Allardyce's future at West Ham with club hero Paolo Di Canio linked with his job after the Italian resigned at third tier Swindon Town four days' ago.
"It's a bit of an old hat story because we've been talking about it for such a long time," Allardyce, whose direct style of play does not appeal to many West Ham fans, told reporters.
"But you haven't been talking about David Moyes in the same context.
"His contract is up at Everton this year and it doesn't look like there has been any negotiations.
"I've clearly explained to everybody several times this is a both parties' agreement. Both parties will sort it out privately and confidentially when the time is right."
Allardyce has yet to discuss a new deal with West Ham co-owners David Sullivan and David Gold, but they have said talks would start when the club's Premier League safety was secured.
West Ham, who host Tottenham Hotspur on Monday, are 11th in the Premier League with 30 points from 26 games. Everton are 12 points and five places above West Ham.