The Serbian midfielder has fallen out of favour under Ole Gunnar Solskjaer this season and has been an unused sub five times already.
He is ready to quit Old Trafford but would like to stay until the end of the campaign to finish off the remainder of his contract, says The Sun.
Inter chief Antonio Conte is desperate to add another midfielder to his squad after an impressive start to his reign.
He has made the ex-Chelsea ace, who is seen as a cheaper option than others around Europe, his top transfer target.
It is understood talks have already begun between Matic's representatives and Inter over the possibility of a deal.