Jones’ contract with Manchester United expires at the end of the season and speculation has been rife that he could leave Old Trafford.
The England international is one of several United players whose deals run out in the summer and is currently free to speak to potential suitors.
The vacant manager’s role at the Theatre of Dreams has further cast doubt over Jones penning a new deal with the Red Devils.
Jones is keen to sign a new contract but knows the decision over a new deal ultimately doesn’t rest with him.
“I’m very settled – I’ve been settled for a long time here,” Jones told Sky Sports News.
“Ever since I walked through the door I was made to feel very welcome.
“I’ve thoroughly enjoyed my time – it’s been great and long may it continue. Of course, I do [want to stay] – it’s Man United.
“This club has been part of my life for many years now. I love the club, the fans, the players. We’ll see what happens. It’s not down to me what happens.”
Jones joined Manchester United from Blackburn in June 2011 for a fee of £16.5million.
The 26-year-old has made a total of 207 appearances for the club, scoring five goals in the process.
Jones has first-team football hard to come by this season, amassing a mere 15 appearances.
United return to action this afternoon, travelling to the King Power Stadium to take on Leicester City.