Matt Hughes of the Times reported on Tuesday that Appleton had rejected the Red Devils' approach in favour of a longer stay at Oxford, who are on track to make a challenge for promotion from League Two this term.
Appleton started his playing career in the Manchester United academy, but the ex-midfielder left Old Trafford for Preston North End in 1997 after making just two senior appearances for the top-flight outfit.
Last month, the Mirror's John Cross reported United are seeking a new head of youth player recruitment following the announcement 16-year veteran Derek Langley is set to leave, having become "disillusioned with the setup."
The Us are currently third in League Two after losing just four times this season, the joint-fewest of any club in England's third-tier competition, alongside Portsmouth.
Guardian contributor Rupert Fryer recently noted the Oxford boss is willing to incorporate innovative technology and analytics in his management approach:
Rupert Fryer @Rupert_Fryer
As we're on TV, look closely and you can actually see the GPS trackers on the backs of the #oufc players.2016-1-14 20:30:00
Rupert Fryer @Rupert_Fryer
@_Liam_OBrien club. Appleton loves his analytics.2016-1-14 20:40:49
As confirmed by Hughes, United are having little luck in their bid to find a new figurehead for the academy after Tottenham Hotspur’s head of coaching and player development, John McDermott, turned down the role last month.
Appleton has earned praise for guiding Oxford to the fourth round of this season's FA Cup, where his side suffered a 3-0 home defeat to former club Blackburn Rovers. However, Oxford did mastermind a 3-2 defeat of top-tier outfit Swansea City in the third round, after which the manager spoke of his joy at the result, per the Press Association:
PA Dugout @PAdugout
.@OUFCOfficial's Michael Appleton saluted "magnificent" show after sending @SwansOfficial out of FA Cup #oufc #SCFC https://t.co/rt6zgFPaIf2016-1-10 15:29:59
Metro's Sean Kearns described the United academy as "failing" after their under-18s slipped to the bottom of the Premier Academy League's north division this season, winning just three of their 19 games.
However, the Red Devils' youth ranks could hardly be deemed total "failures" after winning the Under-21 Development League's Division One title last term. The under-21s are now second in this season's table with three games in hand over leaders Sunderland.
It's also pointed out by Kearns that Brian McClair's departure from the role of academy director in February of last year appears to have stunted their progress, with the club failing to appoint a successor since.