David Kent of the Daily Mail reports the Red Devils are keen to tie the defender to a new five-year deal at Old Trafford which would see his salary rise to £75,000 a week, 50 percent more than his current £50,000-a-week wages.
The centre-back's current contract will expire in 2016, but Kent claims there aren't expected to be any obstacles to Jones' recommitment, with Jones presumably happy to stay on at his current club.
With the departures of Nemanja Vidic, Rio Ferdinand and Patrice Evra this summer, Louis van Gaal's defence is seeking new leading figures. Ex-United icon Gary Neville wrote of Jones' need to step up in such circumstances and others prior to the 2014-15 season in a column for United's official magazine (via the club's website):
Big personalities like Patrice Evra, Rio Ferdinand and Nemanja Vidic have gone, and new leaders and characters need to emerge in the dressing room.
This is now the opportunity for [the likes of] Phil Jones, David De Gea, Juan Mata, Ander Herrera - players who've been signed - to become leaders and develop the mentality that they want to take over the mantle.
Jones arrived at Old Trafford from Blackburn Rovers in 2011 and has steadily grown as an important squad member despite seeing his playing time divided between duties at centre-back, right-back and as a deep-lying midfielder.
However, that malleability may work to his advantage under the tutelage of Van Gaal, who will seek mobile, athletic assets to fit the 3-5-2 system in which Jones has so far played a prominent role.
So far this summer, Luke Shaw and Marcos Rojo have arrived as defensive reinforcements to the United roster, but Jones will be hoping to have impressed enough to retain his spot in the starting XI.
The 22-year-old should retain an important spot in Van Gaal's plans, too, capping off an impressive 2014-15 pre-season schedule with a man-of-the-match display in his team's final outing against Valencia.
In his three years with United, Jones has made 105 total appearances, per his official club profile, but with Ferdinand and Vidic now at Queens Park Rangers and Inter, respectively, demand for him to perform is all the higher.
The England international began his Premier League campaign with a 2-1 loss to Swansea City last Saturday, but even in that defeat, Spanish journalist Sergi Dominguez highlighted Jones as one of the home side's better performers:
Even with the prescribed bump in wages, Jones wouldn't be anywhere near the club's top earners—Wayne Rooney is raking in four times that amount—but it's nevertheless a sign that United value his skill set.
Life under Van Gaal should give Jones the opportunity to claim the regular role in "central defence" he's been craving for so long, but with new tactics and stratagem in tow, it's another change the youngster must adapt to.