The guitarist previously appeared in the band's video for their non-album single 'RU Mine?'.
"I think they're really good, and I think Alex Turner's a very, very talented kid," Jones told Digital Spy.
"I'd like to do be a bit of guitar with them guys. I'll play on anyone's record, to be honest with you. Me and Alex, we text each other quite a lot. He's a good kid."
Of Turner's lyrical ability, he added: "He's just got a gift for doing it and not many people have that gift. It's just a gift that some people have. He's one of them guys.
"He's got that real talent of writing lyrics and making it sound like an image. You see what he's writing - you see the image of what he's writing."
Of his cameo in the Arctic Monkeys video, Jones said: "You need tough skin if you wanna read the comments on YouTube. I actually looked on their video - I was watching it and reading some of the comments
"They're like 'Who's that fat bastard at the beginning?'. None of them have any idea who I am. They think I'm some fat f**king idiot talking in a microphone."
Watch the Arctic Monkeys 'RU Mine?' music video below: