Liverpool are second in the Premier League - one point behind reigning champions Manchester City with six matches remaining.
Hasenhuttl has had a huge impact for the Saints since taking charge of the first team, helping them climb out of the relegation zone after a dismal first half of the 2018-19 campaign.
Ahead of Liverpool's arrival on the south coast, Klopp revealed that he came close to buying Hasenhuttl while he was working in the Bundesliga with Mainz.
"I thought about signing him as a back-up striker for different situations when I was the manager at Mainz," Klopp told Sky Sports. "That would have been funny!
"Each little step in his managerial career, he has really worked hard for and deserves all the praise for it.
"It was a smart decision by Southampton to go for him."
Liverpool are chasing their first league crown for 29 years, while also plotting a course through the latter stages of the Champions League.
Four successive wins across all competitions have seen the Reds get back on track after an inconsistent start to 2019 and they will be expected to secure another three points against the Saints.
The 51-year-old coach might have one eye on his team's European clash with Porto next week, however, as the fixture list begins to pile up and tensions continue to rise in their bid for silverware.