The £3.75million signing was dropped from the next four matchday squads following an underwhelming performance in the 5-0 loss to Manchester City on the opening day of the campaign, but has since redeemed himself with a string of fine performances.
Cresswell has scored two league goals thus far, and is looking to reestablish himself as a starter for Manuel Pellegrini’s side.
He isn’t the only one the club wants to offer a new deal, though.
The Sun claims the Hammers will also look to renew the deals of Mark Noble, Lukasz Fabianski and Michail Antonio as they are being looked at over the next few months as they enter the last 18 months of their contracts.
West Ham are aiming to finish in top-seven this term, and have won three, drawn three and lost two of their opening eight games of the campaign.
They are planning for the long-term from the look of things, and while they are expected to keep making necessary squad changes during subsequent transfer windows, keeping the core of the team going forward will do them a lot of good.