The 32-year-old has not played since leaving United at the end of the 2022-23 season, with his last appearance coming 12 months earlier in a 3-0 win over Brentford.
Jones, who won 27 England caps, joined United from Blackburn in 2011 but struggled with injuries throughout his career.
“My career finished shorter than I would have liked,” he told BBC Radio 5 Live.
“[I’m] glass half full. [I have] completed my A licence and I want to get out there and challenge myself in coaching.
“Ultimately I want to take charge of a team. I am determined to get there.”
During his 12 years at United, Jones won the 2013 Premier League title in Sir Alex Ferguson’s final campaign as manager.
He also won the FA Cup in 2016, the League Cup and Europa League in 2017 and the Community Shield in 2011 and 2013.
Jones, who came through the youth ranks at Blackburn and made his senior debut for Rovers in 2009, added: “I did everything I could [to return to playing] but with so many rehabs I was coming back from, it has an effect on you and your family.”
Speaking previously in 2021, former centre-back Jones said he had “been through hell and back” after struggling with injuries, and lockdown following Covid-19.
Last September, he reportedly returned to United, external as a youth team coach.