Manchester United winger Nani has arrived in Istanbul to complete a move to Fenerbahce.
Liverpool are set to confirm the appointment of Sean O'Driscoll as assistant manager on Monday.
Allardyce and the club have always maintained a new deal is on the cards but will not be rubber-stamped until another season of top-flight football is guaranteed.
Allardyce, whose current deal expires in the summer, says it will take five more points before both parties are happy relegation is no longer a real threat.
He said: "I want us to get safe and then if the contract's already there and ready to sign, I'll sign it, move on and get ready for next season.
"I'm not so sure we have to wait until we're mathematically safe. I think if we get to 38 points both parties would say that's going to be enough this season.
"Hopefully we can get to 38 points as quickly as we can, then we'll have a few games left it achieve more than 40 points if we can."
West Ham have won just twice in nine league games, and Allardyce said: "It's been a little disappointing recently, not from a contract point of view but from a results point of view.
"I'm disappointed we haven't already clinched safety because I think we should have done based on our performances.
"Our lack of concentration and, on some occasions, our lack of goals has made us linger on this subject.
"We all want to get it out of the way, done and dusted and focus on hopefully another season in the Premier League."