That defeat has seen fans turn on the 54-year-old with many desperate for the club to appoint a manager more in line with their attacking traditions.
Yet Spanish website Don Balon claim Manchester United are ready to turn to Simeone if Mourinho is axed at the end of the campaign.
Mourinho only signed a new contract at the start of the year.
But the former Chelsea boss is looking increasingly subdued at Old Trafford.
PSG are not helping matters either with the Ligue 1 giants supposedly keen for Mourinho to Unai Emery’s replacement.
Emery is likely to pay the price for his failure to win the Champions League.
Mourinho is their No 1 choice to take with club chiefs on the lookout for a blockbuster name to manage the likes of Neymar, Kylian Mbappe and Edinson Cavani.
And Don Balon say United’s own hierarchy are huge admirers of Simeone.
Yet prising the Argentinean away from the Wanda Metropoliticano may be difficult.
Next year’s Champions League final takes place in the stadium, which only opened at the start of the season.
And Simeone may opt to sit tight, with the former Inter Milan midfielder determined to steer Atletico to the prize.
Talk of the 47-year-old moving to Old Trafford is nothing new.
Earlier in the year, speculation was rife he wanted the job after supposedly snubbing an approach from Chelsea.