The Sun says Mourinho travelled to Italy last night and reports suggest an agreement could be reached within hours.
But the Serie A club's president Massimo Moratti is keen on Mourinho.
A senior source at Inter recently said: "Moratti is a great admirer of Mourinho who he sees as one of life's achievers - just like himself.
"The belief is that it will not take too long to reach an agreement with Mourinho to become the new coach of Inter."