The 33-year-old's contract is set to expire at the end of the season and last month SunSport reported he was playing hardball over a new deal.
But the winger turned full-back is keen to extend his stay at Old Trafford and win more trophies in Manchester.
Speaking after his side's 4-1 hammering against Fulham, Young insisted he is as fit as ever and would love to stay at the club.
He said: “I feel as fit as when I was 21 years old. As long as my legs can keep taking me up and down the pitch, I'd love to stay here.
“I'm 33, nearly 34 now, that's not changed for me. I still want trophies, still want to win things and that's what everyone in the squad wants. Everyone wants to win.”
Last season Young was rewarded with an extended deal for his performances- but as he approaches 34 there is no denying his boss Mourinho will be eyeing up replacements as he plans his long-term future.
But who are five of the key targets and where will they fit in at Man United? Find out below…
Mourinho could turn to Juventus full-back Alex Sandro.
The pacey Brazilian has been impressive for the Old Lady since moving from Porto in 2015.
And the full-back is also a threat offensively – having netted nine times in 88 Serie A appearances for the Turin outfit.
Sandro has been linked to Chelsea and United for a number of transfer windows – but Mourinho will have to snap him up quickly as he is reportedly set to offered a lucrative new contract by the Italian club.
Another potential Young replacement is Tottenham's Danny Rose.
In an exclusive SunSport interview, Rose made no secret of his desire to leave Spurs at the beginning of this term.
He was critical of his club's lack of trophy winning and said he felt desperate to move on and win silverware before it is too late in his career.
And he could move United under Jose Mourinho, with the Portuguese a coach a proven trophy winner.
Rose also often finds himself playing second-fiddle to Welshman Ben Davies in the line-up and may want to move to seek regular first team football.
Mourinho could also turn to Celtic starlet Kieran Tierney as a long-term replacement.
Scotland starlet Tierney has been tipped as the man to lead the Hoops into the future, but his outstanding quality is attracting interest south of the border.
And according to the Times, the Portuguese boss recently sent scouts to watch the full-back in Scotland.
The 21-year-old has been outstanding for the Scottish side under Brendan Rodgers and recently has been monitored by Fulham and Everton.
Mourinho could also look to replace Young with highly rated Augsburg full-back Philipp Max.
The 25-year-old enjoyed a very productive season in the Bundesliga last term – notching up the second most assists in the league with 12.
However Mourinho will have to fork out £35million for his services – as he currently has four years left on his deal.
Max made his name at the Schalke and Bayern academies before signing for Augsburg.
Lastly, Man Utd could be poised for a move for Barcelona and Spain left-back Jordi Alba.
The experienced defender has yet to be offered a new deal by the Catalan giants – and SunSport reported that United and City are keen to sign the 29-year-old.
Alba himself admitted it was "strange" he was not offered a new deal, and there is no doubting the Old Trafford faithful would be delighted if this move were to materialise.
If Young was to be let go by the Old Trafford top brass, there is no doubting he will be remembered as a great player for the club.
He has been a loyal servant for Man Utd since his £17million move from Aston Villa in 2011 – netting 14 goals in 161 Premier League appearances for the club.
And he has continued to be a useful asset to the team – having changed position from a winger to a full-back over the last couple of seasons.
His latest feat came on Saturday when he scored a stunning goal against Fulham.
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