Reina could return to the Liverpool side on Sunday for their match with Newcastle United, but Jones believes that he has done all he can to retain his place.
"Everyone wants to play. I have just tried to do as well as I can and I've been fairly happy with how things have gone," he said.
On competing with Reina for a starting place, Jones added: "We have a good, friendly rivalry. Every day in training we are trying to beat each other and stake a claim as much as we can but you only get those chances when you play."
The 30-year-old has only made 11 appearances for Liverpool since he joined the club from Middlesbrough in 2010.