Despite signing for Inter just 18 months ago, D'Ambrosio, who has gone on to make over 40 appearances for the Serie A outfit, is set to depart this summer.
Now, the Upton Park hierarchy are expected to meet with the player's representatives in order to work towards a deal.
Having been pushed down the pecking order at the San Siro after the club signed Martin Montoya from Barcelona earlier in the summer, he is understandably eager to secure first team football
Inter Milan are understood to be willing to sell D'Ambrosio for a decent price, and his versatility as both a defender and a midfielder certainly makes him a very attractive proposition for the Hammers.
The Italian made 23 appearances for Inter last season, fashioning 20 key passes - including two assists - while winning 53% of his attempted take ons.
Reports - such as those from TMW - suggest London rivals Tottenham Hotspur are also keeping tabs on the situation, while the Hammers will also have to fend off interest from Roma, who have contacted Inter regarding the 26-year-old's availability.