The former West Ham boss was reportedly left considering his future after the club parted company with the only member of the backroom team at the Stadium of Light that Allardyce brought in upon his arrival, Mark Taylor, according to the Mail.
Taylor helped the Black Cats boss during the January transfer window as they went on to sign the likes of Jan Kirchhoff, Lamine Kone and Wahbi Khazri who would all prove instrumental in keeping the side in the Premier League.
But after letting Taylor leave earlier in the year - in what the Mail suggest are circumstances that Allardyce himself does not have a full understanding of - it appears that Big Sam was also preparing to potentially follow him out the door.
Had Allardyce left in March, it seems highly possible that the relegation fight would be going down to the final day, if Sunderland were not relegated already.
Since April, the Black Cats have lost just one of their seven games while also winning three, including emphatic 3-0 victories over both Norwich and Everton as well as a dramatic 3-2 win over Chelsea.
And with the side keeping four clean sheets during that run, it is quite obvious the impact that Allardyce has had on the team, and thus, it is fair to say that their chances of survival would have been much slimmer had the boss walked out.