Jones has formed a strong partnership with Eric Bailly at the heart of United's defence and has played every minute of their three wins since the Premier League season began on 11 August.
The 25-year-old's form has prevented United's summer arrival Victor Lindelof from making his league debut. Jones and Bailly have ensured a clean sheet in every game as the 20-time English champions sit atop the table two points clear of the chasing pack.
According to the Mirror, the United defender is now a doubt for England's double-header World Cup qualifying matches against Malta and Slovakia. The Three Lions take on the former away from home on Friday night (1 September) and the latter three days later at Wembley.
Mourinho will be hoping that Jones' injury is a minor one as the Portuguese manager has hailed his qualities as a central defender. The England international is likely to remain first choice once the season resumes after the upcoming international break, if he remains fit.
Jones has been injury-prone since his arrival from Blackburn and has missed big chunks in recent seasons owing to a range of injury issues. Mourinho is aware of his troubles and believes the player needs constant monitoring from the medical team in order to remain injury-free throughout the campaign.
"He's potentially a very good player, he's still young and at a learning age," Mourinho said, as quoted by the Mirror.
"And now he's complaining about an ankle problem. So he's the kind of player where we need to have him always in our hands with a lot of care from the medical department," the Portuguese coach explained.
"If we manage to protect him from injuries, he is everything I like in a central defender."