The 58-year-old guided the Hammers to promotion from the Championship and Premier League survival in his first two seasons at the Upton Park helm, but has been offered little assurance that his reign will stretch beyond the end of the season.
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"My job is about never being satisfied, I always want to do better," Allardyce told reporters.
"I'm a pain in the arse to the owners, because I've never got enough money, but that's just the way I am. Sometimes they may feel it's difficult to live with, but it's my ambition driving myself and the club forward.
"The highs and lows are massive for a manager, and you have to be big enough to deal with them.
"I'm not begging for a contract and I've never had to - our understanding has always been to see where we are at the end of this season before we talk about a new one, but that was more my idea than the chairmen's."