Allardyce's deal at Upton Park expires at the end of the season and there has been speculation over the last three months that he could well be on his way in the summer.
Many Hammers fans still haven't taken to his long-ball style, and the general belief is that the club need a fresher approach.
But the former Newcastle United manager insists both parties are keen to find a solution.
Sam Allardyce: "We both want to do it, it's just a question of sorting out the dotting of the i's and crossing of the t's.
"As always, that is not as easy a situation as you would like.
"We need to move to this new stadium to compete with the likes of Chelsea, Arsenal and Tottenham in this world.
"So we will hopefully come to a conclusion very shortly.
"I can understand why they don't want to leave Upton Park because they probably came here in their infancy and their dad, uncle or grandad brought them so they've grown to love this stadium.
"But at the end of the day, football has to progress."