Instead, the Special One would prefer if he could target a move for Juventus ace Paul Pogba, or Atletico Madrid's Koke.
Fabregas has been heavily linked with a move to Chelsea in recent weeks, with some reports going as far to suggest that a deal could be imminent. However the suggestion from the Independent is that if the Barcelona midfielder does arrive from the Nou Camp, it would be because the club's board wants to sign him, rather than through Mourinho pushing for it to happen.
The Portuguese boss aggressively remodelled his squad in his first season back at Stamford Bridge by letting fan-favourites David Luiz and Juan Mata leave, while veterans Ashley Cole and Frank Lampard have not had their contracts extended.
That rebuilding is set to continue in the summer window, but there could be friction over the right path to take with Mourinho said to be uncertain over whether Fabregas is the type of player he is after.
Instead he would prefer to swoop for Pogba, the former Manchester United midfielder, or Koke, who is a target for the Red Devils this summer. Barcelona have also been linked with the Atletico ace.
Pogba has emerged as one of the finest young midfielders in Europe since leaving Old Trafford, and would certainly fill the void left by Lampard's departure in the heart of Chelsea's midfield. However he has reportedly been valued at £65 million by Juventus, which would be an issue for Chelsea.
Fabregas faces an uncertain future following a disappointing campaign at Barcelona. He was booed by some of the club's fans towards the end of the season and a poll by Spanish newspaper Marca revealed that 50% of the club's fans wanted him to be sold.
Barcelona are said to be looking to move him on in the summer, and are hoping to secure a fee of around €40 million for him.
Manchester United were heavily linked with him in 2013, however the departure of David Moyes and arrival of Louis van Gaal has cast a doubt over the level of their interest.