Di Michele is currently on loan with the Hammers from Torino.
The 33-year-old told La Gazzetta dello Sport: “My objective is to play more and to score many goals at Upton Park before the season ends.
“Being a West Ham player is a top experience for me and I’d be glad to stay here.
“Obviously it’s up to me because I must play well on the pitch to help the club the best I can.”
