Questions over Allardyce's future at West Ham have continued to linger despite the Hammers boss guiding the club to 10th in the Barclays Premier League following their promotion last summer.
Allardyce insisted in March that he would be penning a new deal "very soon" after productive talks with Hammers owners David Gold and David Sullivan, but the contract that he has been offered is yet to be signed.
The 58-year-old says all that will change next week though following the Hammers' penultimate game of the season at Everton on Sunday.
Allardyce said: "I will be signing my contract very shortly. Early next week will be the right time.
"It's Friday today and we are getting ready to travel tomorrow and we are concentrating on Everton.
"But by early or next midweek I will be looking to put pen to paper."
Paolo Di Canio's departure from Swindon led to speculation that he could replace Allardyce at the end of the season, but Sullivan recently maintained he could never employ the controversial Italian, who has already been snapped up by Sunderland anyway.
The two-month wait for Allardyce to take up West Ham's offer has raised eyebrows, but the former Bolton and Blackburn manager insists the hold-up has been down to wading through vast swathes of legal jargon and the need to secure top-flight survival, rather than because of any problem with the club's owners.
"There were processes we had to go through and put it together in the right way, which it has now," Allardyce said.
"I never thought there would be any problem - and there hasn't.
"There has been some issue with the legal jargon in the contract which I couldn't understand so that has to go to both sides lawyers to agree and then it gets signed.
"The size of a manager's contract is pretty substantial in terms of responsibilities."
Signing Andy Carroll, who is on loan from Liverpool until the end of the season, will be Allardyce's priority once he signs his new deal.
"We would like Andy Carroll to stay and I would prefer that to be on a permanent basis," Allardyce said of the striker, who Gold and Sullivan chose as their West Ham player of the year this week.
Despite all the talk of Allardyce's future, and that of Carroll, the Hammers boss is concentrating on giving Hammers fans what would be just their fourth away win of the season on Sunday.
The east London club travel to Goodison Park this weekend for what will be David Moyes' last home match in charge of the Merseyside club before he departs for Manchester United.
With emotions riding high among the Everton support, who have given Moyes their backing during his 11-year spell at the helm, Allardyce hopes the Everton players will take their eye off the ball.
Allardyce added: "He'll ask himself and all his players to be professional and not to let themselves down first and foremost and not to let the club down on what they've built over a long period of time.
"Most of the players have been there a long time now and have a lot of respect for David. Personally I hope they don't bother.
"That would be great for me if we can get three points by the fact they're playing the game not quite at full tilt, like they normally do.
"At full tilt they're an extreme force to deal with. If there's a bit of easing off there then we'll want to take advantage of that."