The 25-year-old has been in impressive form for the Hammers and has been arguably their best player this season.
The left-back has scored one goal and created 27 chances in 28 Premier League appearances, while having a pass accuracy of 73% and wining 55% of the duels.
Cresswell’s performances for West Ham this campaign have led to speculation that defending English champions Manchester City are interested in his services, as reported by The London Evening Standard.
Allardyce, though, is not worried about losing his star player at the end of the season and told West Ham’s official website: “I wouldn’t have thought there needs to be a new contract because he’s got four years left I think it is.
“So there’s no rush or pressure. It’s one for the chairmen but I doubt there’ll be any action needed. We don’t act on anything that’s all rumour and speculation."
Cresswell joined West Ham from Ipswich Town in the summer of 2014 and has a contract that runs until June 2019.
West Ham are an ambitious club and are not looking to cash in on their best players, although a ridiculous among of money could change their mind.