Allardyce's deal at Upton Park expires at the end of the season and there has been some speculation that he could leave the Hammers in the summer.
But the former Newcastle United manager insists both parties are keen to find a solution.
"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," Allardyce told Sky Sports News HD.
"As always, that is not as easy a situation as you would like.
"You always have to do some negotiations when you are moving into the next contract, just as there were plenty of negotiations over the first contract.
"So we will hopefully come to a conclusion very shortly."
A new deal would raise the possibility of Allardyce overseeing the transfer from Upton Park to the Olympic Stadium, set to occur at the start of the 2016/17 season.
The move has been the subject of resistance from various parties, including some West Ham supporters, but the manager believes it is necessary if the club is to progress.
"We need to move to this new stadium to compete with the likes of Chelsea, Arsenal and Tottenham in this world," he added.
"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."