England's Test team has thrived since Stokes took over as captain nearly a year ago, winning 10 of their 12 matches under him. Moeen said on Friday evening that Stokes' success with England makes him an obvious candidate to succeed the 41-year-old Dhoni as captain, but suggested that a change might not be imminent.
"He's really enjoying himself," Moeen said of Stokes. "CSK is the type of franchise where you come here and you do tend to enjoy yourself and really love playing for this franchise. He's settled in really well. He's a big part of the team with his experience."
Asked if Stokes was part of the franchise's leadership group, Moeen said: "There's no real such leadership group: you have the captain and the coaches, and they talk. If Dhoni wants Ben Stokes' advice, or a chat with him, it's a very open environment in that changing room."
"I think there's a chance [that Stokes succeeds Dhoni]; of course there's a chance, because he's obviously done really well in Test cricket," Moeen said. "But MS is still obviously in charge and he's going to be captain for a while. We have some other guys as well: Ruturaj is a fantastic player with a good head on his shoulders, so it depends on what the franchise wants."
Speaking to Sky Sports, Stokes insisted that his "main priority" was ensuring he will be able to "fulfil my role as fourth seamer" in the Ashes series later this year, which starts on June 16 at Edgbaston. "Great format to come back into bowling again isn't it, T20?" Stokes joked. "I said at the end of [the] Wellington [Test], it's been a very frustrating year - that's how long it's been, bowling with this knee problem. Not being able to fulfil my role properly as fourth seamer has been frustrating."
Stokes has bowled 174.3 overs in his 12 Tests since his appointment as England's permanent captain, but managed only nine during their recent two-match series in New Zealand. Ahead of the Ashes, which starts on June 16 at Edgbaston, he hopes to ensure that he will be able to contribute fully with the ball.
"I've worked so hard over the last month, five weeks, to get to where I am now," Stokes said. "Being able to bowl pain-free, touch wood, has been good. Even [on Monday] night, I went for 18 runs but I was like, 'I managed to bowl an over without any pain in my knee.'
"That's down to a lot of hard work that I've done away from [the game] medically, in the gym, and obviously I've had a bit of help with some cortisone injections, but everything is going nicely. I'll just take it step by step and not look to rush myself in too much, because obviously the main priority for me is making sure that I can fulfil my role as fourth seamer in the Ashes."
GMT 1727 The piece was updated with Moeen Ali's quotes.
Matt Roller is an assistant editor at ESPNcricinfo. @mroller98