Jones has played in the first three of the Reds’ games on Tour 2013 presented by Aon, including 90 minutes in the last two.
He told PA Sport: "I said I needed a good pre-season and I feel I am getting one. I am getting sharper each game. Hopefully, by the time the season comes round I will be bang on.
"Pre-season is massive building up to the new season. We have a new manager, there is a good vibe and I am enjoying it.
"The training has been as sharp as nails. There is a willingness to impress the new manager and that is the case with all the players, not just me. It has been competitive. It is an exciting few months ahead and I am looking forward to it."
Jones’ long-term role in the United team is still the subject of much interest and he was asked whether he was happy to be cast as a utility man.
"As long as I am in the team it doesn't matter whether I am in goal," Jones insisted. "Of course, towards the middle and end of my career I will want to start cementing a place in a certain position but at the moment I am happy.
"I have said from day one I see myself as a centre-back. But if I am asked to play in midfield or at right-back I am happy to do so."
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