The Aussie has recently turned 31 years of age.
Jones told Liverpoolfc.com: "I don't have any specific targets for the rest of my career, but I would like to possibly get to 40.
"There are plenty of 'keepers about that are in and around that age and if you can do it, you've got to make the most of it and play for as long as you can because once it's gone, it's gone and that's it - it just becomes a memory.
"You might as well play for as long as you can, so if I can get to 40 and still be playing then brilliant.
"I've got a few years to catch up to the likes of Friedel, Schwarzer and the like, but before them there was Lehmann, Seaman and David James that have played on for the same amount of time, so I don't see why I can't as long as I keep myself in shape and, touch wood, there are no injuries."