While Saints were beaten last night by Arsenal, Hoddle was impressed by Hasenhuttl's team for the weekend's FA Cup triumph over the Gunners.
Hoddle says the recent form resurgence of Southampton has come from Hasenhuttl's bold tactics - which include the rare approach of playing twin strikers in attack.
Hoddle said on his podcast, ' The Glenn Hoddle Footy Show': "They really are a dangerous side to play against. They've gone through a lean spell, but they've come out of that again. They have a system that works for them. They're playing two up front for as many times as they can - which is a little bit different nowadays - and they put people on the back foot.
"They press well. They're well organised and they have some creativity in there as well."
He continued: "If there is somebody outside the top five or six teams that might win this, I think Southampton might be the one I'd put a few shekels on as an outside bet."
Hoddle also praised Hasenhuttl for the way he's handled things amid a move from the club's owner to find a new buyer.
Saints remain up for sale after offers were invited by Chinese businessman and majority stakeholder Gao Jisheng last year. The Austrian is the third manager to be employed under Gao following his takeover, succeeding Mauricio Pellegrino and Mark Hughes.
Hoddle admits the situation could be a concern for Hasenhuttl, who will know any new owner may want to bring in their own manager to take charge.
He continued: "Yeah, it can be, unless you have a good relationship with the people coming in. (But) whomever comes in I can't see anybody, unless the one they have is nailed on and a part of their journey from another club or wherever, you certainly wouldn't want to change the manager for the way they're playing and the job he's done.
"What has impressed me most about Hasenhuttl is when there's been a poor run, he's turned the team around - and quickly. He has shown consistency.
"But there's been a problem with Southampton: they've always sold their best players. You look at the players they've produced and they've gone on to be big stars at bigger clubs. Managers have done the same (Mauricio) Pochettino, they moved on from there.
"I think it's been a pattern for the Saints and it's made it difficult for them. But they keep reinventing themselves. I've been impressed with them this season."
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