The Red Devils want to sign the Italy international midfielder this winter after not firming up interest during the summer window, per Dan King of The Sun.
Mourinho is said to be frustrated by United's inability to land many of his prime targets this summer. However, he does think "Pellegrini fits the profile of a box-to-box midfielder to give the team a more dynamic link between attack and defence."
It's a reasonable assumption since the 22-year-old has been steadily emerging as a potential star in recent years. He helped himself to three goals and five assists last season as Roma reached the last four of the UEFA Champions League and finished third in Serie A.
If he made the jump to Old Trafford, Pellegrini would offer a goal threat and valuable direct running in combination with steady passer Fred and holding player Nemanja Matic.
Whether United make interest concrete this time will depend on Mourinho's relationship with chief executive Ed Woodward. Mourinho downplayed rumours he is at odds with Woodward during a short and terse press conference on Friday, according to BBC Sport.
However, King noted "Mourinho has told friends he is frustrated," while he's also been left "puzzled by the failure" to acquire Tottenham Hotspur centre-back Toby Alderweireld.
Despite any trouble behind the scenes, Mourinho may have enough motivation to push for Pellegrini, especially given concerns over Paul Pogba. The United captain has been largely inconsistent since becoming the club's record signing on Mourinho's watch in 2016.
With so much uncertainty engulfing Mourinho, it's difficult to imagine he has transfer targets in mind for January. However, if he is backed over interest in Pellegrini, it will be a sign United aren't ready to give up on their embattled manager just yet.