Rashford is now Manchester United's main forward due to the serious injury suffered by Ibrahimovic, and the England global will hope to go some way to convincing the powers that be at Old Trafford to resist signing Griezmann when the Red Devils face Celta Vigo in the first leg of their Europa League semi-final on Thursday (4 May).
Mourinho's pitch to the player will be all about becoming United's talisman, building the team around him, making him someone who the club's supporters will idolise as he helps restore the team to greatness.
United have surveyed the competition in the battle to sign Griezmann and believe they hold the majority of the aces.
Griezmann's reputation as one of the world's best forwards has grown since moving to Atletico Madrid in 2014 from Real Sociedad.
One of the biggest shortcomings faced by Manchester United throughout this season has been squandered chances.
And United won't balk at the figures, having committed a similar amount to last summer's signing of Paul Pogba from Juventus.
Following Zlatan Ibrahimovic's long-term injury and a lack of goals throughout the season, the Red Devils are said to be looking for a prolific striker for the next campaign, but there has been no clear indication as to who it will be.
Last week, the Independent reported that Chelsea would rival Premier League rivals Manchester United in the race to secure Griezmann's signature - but it may well be a pursuit that we're priced out of.
"Antoine doesn't want to leave the club at any cost". They know they have the machine in place off the pitch to deliver that, but it might need the signing of Griezmann to ensure that Mourinho is able to make it happen on the pitch too.