Allardyce will not be in charge of the Hammers next season after his contract was not renewed, as announced on the club’s official website on Sunday.
The Englishman was appointed the West Ham boss in the summer of 2011 and guided them back to the Premier League.
Cresswell, who joined West Ham from Ipswich Town in the summer of 2014, has admitted his disappointment at Allardyce’s departure.
Been a disappointing end to the season but just want to thank everyone for your support all year round, week in week out @whufc_official— Aaron cresswell (@Aaron_Cresswell) May 25, 2015
Also to the gaffer who give me the opportunity to play for the club.. And has been brilliant with me..— Aaron cresswell (@Aaron_Cresswell) May 25, 2015
Cresswell was one of the best players in the Premier League this season and has been linked with a move away from Boleyn Ground in the summer transfer window.
According to a report in The Daily Mail earlier this month, Chelsea and Manchester City are both interested in the 25-year-old left-back.
In 38 Premier League appearances this season, Cresswell scored two goals and created 34 chances, and had a pass accuracy of 73% and a shot accuracy of 53%.