According to a report from Calciomercato, the Uruguayan midfielder is set to leave Inter in the summer for as low a fee as £6.8 million.
The 29-year-old has been transfer listed by Inter according to the report, and he is eager to leave the get regular game-time.
West Ham made an offer to sign Vecino in January, yet this got rejected immediately by Inter.
The 41-capped Uruguay international has not been at his best recently, making his first appearance of the season last weekend.
Vecino has recently returned from a long-term knee injury that had kept him out of action since last July.
Vecino is still a very good player, and his robust tackling and intensity are two key attributes of his play style, which are also perfectly suited for the Premier League.
He is capable of playing all across central midfield, from deep in midfield, all the way up to as a number ten.
Signing him for just £6.8 million could be a fantastic acquisition for West Ham, with David Moyes looking to add some quality experience to his side.
He could provide cover for Declan Rice and Tomas Soucek, and so there could be a lot worse signings that the Irons could make this summer.
Vecino is also wanted by Napoli, yet it remains to be seen whether the Serie A leaders would want to sell him to a rival, making West Ham the favourites to sign him.