It was reported earlier in the season that Mourinho had placed the Frenchman at the top of his list for potential transfer targets.
Griezmann himself has been ambiguous on the subject of a possible Old Trafford move, simultaneously pledging allegiance to Diego Simeone and expressing a desire to play alongside Paul Pogba in the Premier League.
Neville, during one of his informal Twitter Q&A sessions, urged Mourinho to move for the striker.
The player in Spain I thought united should go for most! https://t.co/hcT96vEpOz
— Gary Neville (@GNev2) December 20, 2016
With both Zlatan Ibrahimovic and Wayne Rooney entering the latter stages of their respective careers, Mourinho will need to consider a viable option to compliment Marcus Rashford at Old Trafford in the coming years.
And Griezmann, who has netted 66 goals in two and a half seasons since arriving at the Vicente Calderon, serves as a tantalising option: devastatingly fast, almost impossible to pin down, wildly energetic and smart both on and off the ball. He is embracing the zenith of his career with reckless abandon, and the prospect of seeing the 25-year-old line up next to Rashford, with Pogba playing just in behind, is truly tantalising.