Rodgers remains among the bookmakers' favourites to become Jose Mourinho's permanent successor at Spurs, despite insisting he is "very, very happy" at the King Power Stadium.
Hasenhuttl will share a touchline with Rodgers on Friday evening when the Champions League-chasing Foxes travel to St Mary's and believes job satisfaction is the most any football manager can wish for.
"In his position, I don't know what he is thinking but it is not about the money any more when you have been a manager that long," said Hasenhuttl, who was beaten by Rodgers in the FA semi-finals less than a fortnight ago.
"It is more about having fun in your job and I think in the moment he definitely enjoys his job at Leicester.
"He has everything he wants. He is successful with a very strong side and they are maybe part of the Champions League next season.
"What more do you want as a manager?"
Mourinho was sacked by Tottenham at the start of last week, with former midfielder Ryan Mason taking charge of the club until the end of the season.
Rodgers has been touted for the vacancy alongside Ajax boss Erik Ten Hag and former Chelsea manager Maurizio Sarri, while RB Leipzig coach Julian Nagelsmann is already out of the running having agreed to join Bayern Munich.
With Spurs struggling to make the top four, Leicester are well on course for a Champions League spot and will arrive on the south coast holding a seven-point advantage over fifth-placed West Ham.
Hasenhuttl believes it would be a "fantastic" achievement should the Foxes return to European football's leading club competition and did not rule out a subsequent repeat of their shock 2016 title success, despite the considerable strength of champions-elect Manchester City.
He said: "They have shown in the past that it is possible, why shouldn't they show it in the future?
"At the moment it is definitely not that easy to be above Man City when you see them playing and see the job Pep (Guardiola) does there. I do not see a lot of teams being competitive over 38 games.
"It can never be the goal for Leicester to go for the title all the time but if they make it into the Champions League this season, they have done a fantastic job.
"And then hopefully they are also so strong to push hard for England in the Champions League."
Southampton go into the game nine points clear of the relegation zone but seeking to improve disappointing form which has yielded just 10 points from a possible 48 in 2021.
Hasenhuttl says Leicester's greater financial clout – as evidenced by Saints being beaten to the signing of Belgium international Timothy Castagne in 2020 – is not a barrier to pulling off a surprise victory.
"The whole club has changed into a club that had some really good opportunities with some financial strength at the back," he said of the Foxes.
"We don't have this strength at the moment – I don't know if we will ever have it.
"I only remember in the summer when we had an eye on Castagne but, as soon as they are in the duel, we have no chance to get him.
"This is exactly what makes the difference between these two clubs but it is not a reason not to go in this game and say we still have a chance to win."