The England international pulled out of Stuart Pearce's under-21 squad for tomorrow's friendly match against Sweden, and the report claims he looks likely to miss United's big match against the La Liga champions at the Bernabeu next week.
Jones did not feature during United's Premier League victory over Fulham on Saturday, and withdrew from Pearce's squad with shingles.
United gave no reason for the defender's absence against the Cottagers, but Pearce revealed the illness behind Jones's absence.
Pearce said: "Jones picked up shingles and there's not a lot we can do about it. It's a shame because it makes us stronger when Phil's here, that's for sure. But it gives someone else a chance."
A virus similar to chicken-pox, shingles typically takes at least two weeks to recover from, making it difficult for the young defender to recover in time to face Jose Mourinho's side on February 13.
The report claims Jones will struggle to return to the United squad in time for the first-leg, but should be back in first-team action by the time the second-leg rolls around on March 5.
Jones had flourished in a defensive midfield role against Tottenham last month, and many expected the 20-year-old to fulfil the same remit against Real Madrid this week.