Allardyce has just six months remaining on the two-year deal he signed at Upton Park and would like to stay at the club beyond next summer and continue his good work.
He has already guided the Hammers to promotion last season and established them in mid-table on their return to the Premier League, but he knows the job is not yet done and is staying focused on securing survival.
Allardyce then hopes to be offered an extension but he is staying calm about the situation, insisting that his managerial record is a great source of confidence.
"We will wait until we are safe and then see," he told The People.
"It's up to David Gold and David Sullivan - it's their call. If and when they want to talk I will be ready to discuss a contract, but there's a long way to go yet because we want to be safe first.
"I am more than comfortable with that and although, of course, it's always important to have a contract, to be in this situation at this stage of my career is not such a desperate plight.
"I've been in management 20 years and now my security is my CV. My security is not looking for a big pay off - it's knowing I have made a good impression on all the clubs I have been at.
"My enjoyment now is knowing I can turn a club round as quickly as I did at West Ham. That gives me great confidence in my own ability and that is the better line to take rather than getting hung up about contracts."