While Moeen has been a consistent presence in England's ODI side this year, he was dropped from the Test side during the New Zealand tour in March but returned for the fourth Test against India in Southampton, where he produced a Player-of-the-Match performance with both bat and ball.
Swann questioned the mindset of both Moeen and Adil Rashid, the players whom he believes will be the key if England are to succeed in Sri Lanka.
"I think it is a big series because after being 4-1 [in the Test series against India] I think it's very easy to rest on your laurels," said Swann. "That will mean nothing if they don't go well against - let's face it - a massively out-of-sorts Sri Lanka team.
"They've had a stinker of a time at the Asia Cup and this is a very good time to play them. I don't think we've got the resources to go out there and really challenge them if we don't believe we have, because I don't believe the spinners are in the right mindset."
Moeen was brought back into the England Test side ostensibly as the second spinner to Rashid and, in the second innings at the Ageas Bowl, was promoted up the batting order to No.3 ahead of Joe Root. He has expressed a wish to continue batting higher up the order and playing the supporting spinner's role but Swann is not convinced Moeen is best suited to either role.
"Mo is still in that [mindset of] 'I'm No.2 spinner I want to bat No.3'. That is not the way to go. If Mo turns up at the airport and says, 'I'm going to go to Sri Lanka and be Man of the Series, I'm going to take loads of wickets and I'll bat No.6 where the team needs me, not at No.3 where I'm not suited' then I think England will win. But I think it's all about getting the best out of the spin bowlers who, let's face it, when you go to the subcontinent are the major players.
"Yes, the Test series is a different form and it's in a different country but it seems with Mo that he's so fragile that he needs confidence-boosting all the time. And I implore him to just come on, grab it with both hands. You're a really, really good bowler and stop worrying about being known as the No.2 spinner. It doesn't make any difference, the ball doesn't change shape because you're the No.1 or 2 spinner, the pitch doesn't change length, the same batsmen are batting. Nonsense."
Swann was speaking at the launch of the Cricket World Cup Participation Plan, in which ECB and ICC hope to use the tournament to inspire 1 million children to play the game, and he feels that, whatever the results may be in Sri Lanka, England are right on track in their preparations seven months out from a home World Cup.
"I think from a one-day point of view, with the World Cup coming here next year, we couldn't be in a better place at the minute because the one-day series against India proved to us that we could beat India in England and come back from a pretty slow start to the series as well", said Swann. "And Eoin Morgan is undoubtedly the best man for the job as skipper.
"He has that team really believing they can do anything from any situation and England are favourites."