The Hammers have been dealt blow after blow up front, with Andy Carroll, Diafra Sakho, Enner Valencia and Mauro Zarate all on the treatment table.
That has left Slaven Bilic with virtually no options in attack, and at least one striker must be signed before Tuesday's transfer deadline.
Now, Sky Italia's Gianluca Di Marzio reports that Milan outcast Matri is poised to complete a move to Upton Park tomorrow, when he will sign his contract with the club.
The 31-year-old spent the second half of last season on loan at Juventus, but after an ineffectual stay in Turin, Matri returned to the San Siro this summer.
Yet with new manager Sinisa Mihajlovic bringing in the likes of Carlos Bacca, Luiz Adriano and Mario Balotelli, Matri has been gradually slipping down the pecking order, making an exit almost inevitable.
Matri is set to join West Ham on loan, most likely for the duration of the season, and will be hoping to settle down in East London following a nomadic part of his career, which has seen him play for four different clubs since the summer of 2013.