The 33-year-old is currently on loan at the Hammers, scoring four goals in 24 appearances.
"As I have already said many times I'd love to stay at West Ham for a few more years," Di Michele told West Ham's official website.
"I feel good at this club and I really hope Torino will let me stay here. But in football you never know what can happen and at this stage my desire can't make the difference. It's up to the two teams to find an agreement.
"I'm also surprised how well I settled down in London," he added. "My wife and my children as well, we couldn't have asked for more. I love London."
West Ham have an option to sign Di Michele on a permanent basis, according to reports.