Samuel Luckhurst of the Manchester Evening News reported the Red Devils might focus on Bale or Arsenal's Mesut Ozil, with Griezmann reportedly preferring a transfer to Barcelona. United manager Jose Mourinho is motivated to purchase a world-class attacker, and Bale has been on the club's radar for years.
Per Luckhurst, Griezmann and his family have met with Barca to discuss a switch to the Camp Nou, scuppering chances of moving to Old Trafford. The Frenchman has previously voiced concerns about a transfer to England due to the weather, and he is settled in Spain after marrying his girlfriend last summer.
However, Spanish outlet Diario Gol (h/t Lee Astley of The Sun) recently reported Mourinho has gone off the idea of purchasing Bale and has told Real Madrid he has reservations about the Welshman's fitness record.
Bale's absences have seen him lose credibility in the Spanish capital, and a move to the Theatre of Dreams would give the attacker a huge stage to relaunch his stuttering career.
The 28-year-old remains a global superstar, but his productivity has evaporated after suffering persistent injury.
The former Tottenham Hotspur winger has only three goals and assists to his name in La Liga and Europe this season.
United have experienced a good start to the campaign this term, but the outstanding form and flair of Manchester City has negated Mourinho's results.
The Red Devils lack the creativity of their crosstown rivals, and the capture of Bale would give the Stretford End the excitement they crave.
Miguel Delaney of The Independent reported Mkhitaryan could return to former club Dortmund after being frozen out of the first team by the Special One. BVB have shown the "strongest interest" in the Armenia international who has failed to find his best form since leaving the Bundesliga.
At 28, Mkhitaryan's lack of impact will have spooked his manager, and it is now unlikely he will adapt to the rigours of English football and Mourinho's defensive tactics.
Per the club's official website, Mourinho explained why he has been excluding the Armenian:
"I can only have six [outfield] players on the bench and I try to have some balance on the bench – I had two defenders and [Daley] Blind who can play in different areas. I had Ashley Young to cover me all of the wing and the wing-back position.
"I had [Ander] Herrera as a midfield player, Zlatan [Ibrahimovic] as a striker and Marcus [Rashford] as a second striker and winger. I played [Anthony] Martial, [Juan] Mata and [Jesse] Lingard in the team. To have Micki means that I don’t have one of them and, in this moment, I believe the other ones they deserve [the chance to play]."
Bale would be a suitable signing if a spot in the attack emerges, with pace central to Mourinho's formation.
Griezmann would have been perfect for the club last summer, but with United's needs evolving as Marcus Rashford and Anthony Martial develop, the capture of Bale makes tactical sense.
The Wales international has something to prove once again after a trophy-winning career at Los Blancos, and he could provide the stardust to light up the Theatre of Dreams.