The trialist rounded off a 5-1 triumph at the Silverlake Stadium after Marcus Browne’s first-half double, Steve Seddon’s strike and a Cameron Brannagan penalty set the U’s on their way.
Jones played the final 30 minutes at Eastleigh after getting an hour under his belt at Hungerford Town the night before, with his whipped effort from 18 yards the pick of the goals.
The winger is training with United following his release by Coventry City at the end of last season and assistant manager Short wants him to stick around.
“I’d love him to join the club and he looks as though he’s quite happy here, so hopefully that will get done,” he said.
“I know his history, he’s had his injury problems, but he looks really hungry.“He’s making up for lost time, he just needs to get his fitness back and he’s getting there.
“He came to Spain (on United’s pre-season training camp) and I was really impressed with him.“It was a really gruelling week and one of the hardest pre-seasons I’ve ever witnessed.
“He coped really well, considering the injuries he’s had he didn’t fall short at all.
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“It doesn’t matter how much running you do in pre-season, when you come to the games you feel it and he looked very sharp.
“He was tracking back defensively and looks a real threat in the final third.”
United recorded five wins out of five in their pre-season friendlies against non-league sides ahead of three games against English Football League opposition.
The victory over Vanarama National League outfit Eastleigh was the most impressive of all as Karl Robinson fielded his strongest available starting line-up.
The hosts began brightly but the U’s soon took control, with Browne scoring twice in six minutes midway through the half.
Danny Whitehall halved the deficit early in the second period, only for Seddon to quickly make it 3-1 from Browne’s cross.
