The talented full-back is being lined up as a replacement for Filipe Luis.
It was reported by the BBC that Luis cost the club £15.8 million in July last year.
Unfortunately for Luis he has spent much of it on the sidelines. The Brazilian has failed to overcome Cesar Azpilicueta in the left-back position and has started just 12 Premier League games this season.
His lack of action recently saw him linked with a move back to the Vicente Calderon by the Daily Mail.
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.
Now ESPN are reporting that Jose Mourinho has his eyes set on the player to replace Luis, should they decide to send him back to the Spanish capital.
Cresswell has played 35 times for The Hammers this season scoring one goal and was even mentioned regarding an England call-up last month.