The Frenchman has made an immediate impression in pre-season, and Cresswell is anticipating having to share one duty with him next season.
The talented Frenchman has been acquired from Marseille this summer and has hit the ground running in new surroundings, impressing during his first outing in a friendly meeting with Southend United.
He netted twice in that game, one a delightful free-kick, while he also played a role in the third goal as his cross was turned into his own net by a Southend man.
Cresswell says everyone in the West Ham squad is now talking about the summer recruit and expressing excitement as to what he will bring to the fold.
"Since Dimitri arrived in Ireland he has looked some player,” he told whufc.com.
“I wasn't there on Saturday, but the boys have been talking about how good he was and how good a signing he looks to be for us. It's one we're excited about out, and the fans are too."
Sharing free-kick duty
With the new recruit having caught the eye in training and his first game, it seems Cresswell’s role as free-kick taker may be in doubt next season.
The full-back impressed last season by regularly testing opposition keepers with his dead-ball ability, a spectacular strike against Stoke City being a particular highlight.
He says he is not ready to surrender that responsibility to Payet just yet, although he concedes that he many have to share the duty next season.
"I think there'll be a bit of competition for the free kicks now,” he added.
“Hopefully he can take the right-sided ones and I can have the left-sided ones.”