The centre-back has not managed a single minute this season, with manager Solskjaer preferring summer signing Harry Maguire - now the world's most expensive defender - and Victor Lindelof in front of David de Gea.
Jones made it to the bench for the narrow Premier League victory over Leicester City and could come into selection contention when United begin their European campaign against Astana at Old Trafford on Thursday.
It is the first of three matches in the space of a week for the Red Devils.
"There are players like myself who've not been involved as much, but it's a chance for everyone to get games," Jones told United's official match programme.
"It's a busy period when all the games come thick and fast, when you need a big squad with everyone ready to fight. But it's a period we relish."
Eric Bailly's knee injury and Chris Smalling's loan move to Roma weakened United's centre-back stocks but Jones, a member of England's 2018 World Cup squad, understands it will be difficult to dislodge Solskjaer's regular starters.
"Since I came to this club – when I walked through the door – I knew I wasn't just going to walk into the team and expect to play," the 27-year-old added.
"Today's no different. Of course I want to play, but we've got some quality players in that position. I'll wait for my chance and hopefully I'll get a chance sooner rather than later."
Jones could be set to start alongside 21-year-old defender Axel Tuanzebe, who spent last season on loan in the Championship with Aston Villa as they won promotion via the playoffs, while Eric Bailly remains sidelined with injury.
United's other Europa League opponents in Group L are Serbian side Partizan Belgrade and Dutch outfit AZ Alkmaar.
Solskjaer’s side have conceded just four goals in their five Premier League games so far – the fewest of any side in the competition so far alongside Liverpool and Leicester – keeping two clean sheets.