The report claims the Chelsea boss has his eye on three transfer targets - with Matic the priority.
The Serbian international has been heavily linked with Chelsea since the summer, while Lazar Markovic and Fredy Guarin are also thought to be under consideration as well.
But Matic - who is also a target for Monaco and Paris St Germain - is Mourinho's priority as he looks for a defensive-minded central midfielder.
And the report claims Chelsea's interest in Markovic could be a ploy to help them land Matic.
Both stars play for Benfica, and Chelsea are looking to build up a relationship with the Portuguese club to facilitate the transfer - Manchester United have a similar understanding with Sporting Lisbon.
The report claims Napoli boss Rafa Benitez is no longer interested in Matic - removing one potential competitor for the Benfica star - the Serie A club are looking at Manchester City's Javi Garcia instead.
Matic is reportedly valued at £20m by his club.