Ambrosini leaves AC Milan
Ambrosini has been given a free transfer by the Italian giants after 18 years at the club and Sam Allardyce has identified the midfielder as a summer target.
The 36-year-old also has offers from Major League Soccer clubs in the United States but agent Moreno Roggi has revealed that neither this nor retirement are options his client is considering.
"Obviously Massimo wants to continue," Roggi told the Calciomercato website.
"His preference would be overseas clubs, but if an offer did come in from an Italian side, we would not ignore it completely.
"At this moment we are in talks with West Ham, while we have already ruled out Major League Soccer."
Ambrosini won two UEFA Champions League trophies for Milan, making his debut in 1995 alongside the likes of Franco Baresi, Paolo Maldini, Marcelo Desailly and former Hammers hero Paolo Di Canio.
AC Milan vice-president Adriano Galliani paid tribute to the club's former captain, who went on to make 489 appearances in which he scored 36 goals.
Ambrosini also won 35 caps in a nine-year international career with Italy.
Galliani said on acmilan.com: "I am very sorry to say goodbye to Ambro.
"It is hard to say goodbye. Eighteen seasons together cannot be forgotten and no-one will ever be able to wipe them out. Milan and Massimo Ambrosini part ways. Milan and all Rossoneri fans bid Ambro farewell - he was more than a player, he was a symbol of the club.
"Ambrosini arrived at Milanello as a promising youngster in the summer of 1995 and immediately displayed his talent with an intense work ethic and generosity, two elements that helped him become the player we know, a true champion.
"He came through the ranks under the guidance of great Milan captains, from Baresi and Costacurta to Albertini and Maldini, whom he inherited the captain's armband from in 2009 to himself become a Milan icon.
"His passion for the Milan shirt carved him a space in the hearts of all Rossoneri fans.
"His unswerving professionalism both on the field of play and in training epitomised the man, and his never-say-die attitude came to the fore also during the heart-stopping final match of the season on May 19th between Siena and Milan, his last for the team."