The Guardian state that Jones’ chances of playing against Brendan Rodgers’ side are “remote” - but he could be involved if the Red Devils’ suffer any more defensive injuries between now and the weekend.
As it stands, with Chris Smalling out until Christmas, Marcos Rojo and Jonny Evans should partner each other in central defence against Liverpool - but Jones could make a surprise appearance on the substitutes’ bench.
Jones impressed earlier this season
News that Jones is close to making a full recovery will come as a major boost to Louis van Gaal, whose side prepare to enter the most hectic period of the season without several key first-team stars.
The England international was Manchester United’s best defender prior to his previous appearance, against West Brom on October 20, but the Red Devils have coped well without the 22-year-old in recent weeks.
United's good form
Indeed, the Red Devils have recorded five consecutive wins for the first time since Sir Alex Ferguson left Old Trafford, thanks to victories over Crystal Palace, Arsenal, Hull City, Stoke City and Southampton.
United are favourites to beat their fierce rivals this weekend, before four games in the space of 12 days against Aston Villa, Newcastle United, Tottenham and Stoke City.
Jones, once he proves his fitness, will slot straight back into Manchester United’s defensive line, taking the place of either Rojo or Evans, depending on their respective form.
But with Van Gaal preferring his players to have two full weeks to recover from injury - allowing them to have some game-time with the reserves in the process - it seems unlikely that Jones will return to action until Boxing Day’s clash against Newcastle United.
Angel di Maria
Meanwhile, United’s record signing Angel di Maria is also in contention to make a surprise appearance against Liverpool. Van Gaal, though, will leave it as late as possible before making a decision over the South American.