Jones was promoted to Liverpool's starting line-up for their match at Manchester United, which they lost 3-0, and has remained between the sticks for their 3-1 victory over Bournemouth in the Capital One Cup and a 2-2 draw with Arsenal.
The Australian has only made 26 appearances for Liverpool in all competitions since joining the Merseyside club in August 2010.
"It's been good to be back in the team," said Jones, who missed out on selection in Australia's final Asian Cup squad on Tuesday.
"I always want to play as many games as I can and to be given the opportunity.
"I am happy to go out there, try and do my best to help the team and hope that I do well enough to play the next one.
"I haven't had an awful lot to do in the last three games. I have tried to help the team in certain situations. I have tried to play as much as I can in the way the manager wants me to play.
"In football, and especially with goalkeepers, circumstances dictate how much you do and when you do it. Sometimes you might not have a chance to do anything. I just try and play as best as I can in every aspect.
"I'm playing to get a new contract but I've been playing that way since I signed my first contract. There have been no talks yet but of course I'd like to stay, especially if I’m playing."
Jones' contract expires in June 2016 and, although Liverpool have been linked with the likes of Victor Valdez and Petr Cech, the 32-year-old former Middlesbrough custodian is not interested in leaving Anfield.
"Everyone wants to link other players with us and that is probably not going to change," Jones said.
"If all the speculation was right we would have 40 goalkeepers at the club right now.
"It's something that happens. I don't read newspapers and I don't look on the internet too much. You can't take much notice of it.
"I won't let it affect me. Every game that I play, I will just go out and do my best."
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