Chelsea are believed to be keen on the impressive left-back.
Last week ESPN reported that Chelsea had their eyes on a potential left-back replacement for Filipe Luis. The Brazilian international has struggled to cement a first-team place at Stamford Bridge since his big money move from Atletico Madrid in the summer. It was reported by the Daily Mail recently that Luis could return to Atleti.
Now, a Liverpool legend has advised Cresswell to stay put.
"He's had a fantastic season, I remember early on in the season he and (Carl) Jenkinson played a massive part in West Ham's success.
"He came to West Ham from Ipswich and we wondered whether he could adapt to the Premier League but he has and, in those early months, he was a revelation.
"I don't think a move to a 'bigger club' is right at this moment in time. If he continues the form he showed before Christmas and he can prolong that over two or three seasons, there's no reason why not."
The 25-year-old arrived at Upton Park from Ipswich Town in the summer, in a deal initially thought to be in the region of £3.75 million, rising to £7 million, according to Sky Sports. He has been one of the bargains of the season.
He has gone on to be a big hit with the Hammers faithful, and scored a cracker against Stoke city last weekend.
Time will tell if he does make a big move elsewhere, but Carragher is right. For now, he should stay put.