The Portuguese coach took charge of the Red Devils in the summer of 2016 and won the EFL Cup and Europa League in his first year at the helm.
Victory in the latter competition gave United a return to Champions League football after a season out of the competition.
Mourinho's apparent conflict with the club hierarchy over the transfer budget and his refusal to move out of a hotel had led to speculation over his future.
According to BBC Sport, however, talks have progressed well and it is now just a matter of time before Mourinho commits to remain at Old Trafford beyond the expiry of his present deal in 2019.
The report goes on to suggest that Mourinho's new contract at Old Trafford will run until 2021.