Mourinho is expected to be confirmed as United manager within the next 48 hours with his representative Jorge Mendes and Old Trafford executive vice-chairman Ed Woodward fine-tuning contractual details in a meeting in London on Tuesday.
And despite Van Gaal only being told of his dismissal by Woodward on Sunday evening -24 hours after guiding United to the FA Cup -Mourinho has already pinpointed key targets and areas in need of strengthening in the squad left behind by the Dutchman.
Paris Saint-Germain forward Zlatan Ibrahimovic is understood to be close to agreeing a move to Old Trafford as a free agent in order to be reunited with Mourinho after enjoying a close relationship with the Portuguese at Inter Milan.
And with Mourinho believing that United need to recruit two forwards to bolster his attacking options with captain Wayne Rooney now favouring a move into midfield, Real Madrid striker Benzema has emerged as his top target, ahead of Borussia Dortmund's Pierre-Emerick Aubameyang.
Although the 28-year-old has previously accused Mourinho of being overly-critical of his performances during their three years together at Real, Benzema has since admitted that Mourinho's treatment made him a better player.
“Mourinho criticised me,” Benzema said. “But it was his way of making me react. At the start, it hurt me, but I am used to it now.”
Benzema, who rejected a move to United in the summer of 2009 in order to sign for Real, scored 79 goals in 150 appearances under Mourinho and was regarded as a key figure by the manager during his spell at the Bernabeu.
But while United are prepared to back Mourinho with substantial funds to recruit any player he identifies this summer, senior figures at Old Trafford are aware of the difficulties they face in completing a deal for Benzema.
The former Olympique Lyonnais forward is currently negotiating a new deal at Real that would see him extend his £150,000-a-week contract until 2020 and there is also the issue of the player facing a potential court case in France after being charged with conspiracy to blackmail last November over an alleged attempt to extort money from Lyon winger Mathieu Valbuena using a sex tape. Benzema denies the charge.
United are also aware that Benzema has consistently resisted offers to move to the Premier League, with Arsenal also failing to tempt him from Madrid to England.
With Mourinho also keen to recruit Everton centre-half John Stones and PSG defender Marquinhos, United are expected to spend in excess of £150m on new players this summer in order to ensure that the team can compete for the Premier League title next season.
Discussions between Mendes and Woodward over Mourinho's contract are understood to be well advanced, with a three-year deal on the table for the 53-year-old, who has been out of work since being sacked by Chelsea last December.
Rui Faria, Mourinho's long-term assistant, is expected to be handed a similar role at Old Trafford, potentially forcing Ryan Giggs to accept a lesser role if he is to stay at the club.
Giggs, who flew to Dubai on Tuesday for a post-season holiday, discussed his future with Woodward at United's Carrington training ground on Monday and is aware that Mourinho is keen for him to remain on the staff at United.
The Welshman, who spent two years as assistant manager to Van Gaal, is believed to be torn between staying at the club to work under Mourinho or ending his 29-year association with the club to pursue a career in management.
Giggs has asked for time to consider his position, with both Woodward and Mourinho making it clear that he will be handed a senior position within the new regime.
Original source: Mourinho wants Benzema, Ibrahimovic for United