The 19-year-old joined the Blues in July last year having initially moved to Stamford Bridge as a trainee, and he has impressed since then.
He has featured eight times in the first-team squad and his agent Marco De Marchi has revealed the youngster's intent.
"Borini has not renewed his contract with Chelsea, we are doing the negotiations to reach an agreement," he told tuttomercatoweb.
"The intention is obviously to stay, he has great esteem for the club and the coach."
The Italy Under-21 international spent six years with Bologna as a youth before moving to London.