Midfielder Keita agreed to move to Anfield last summer, and Hasenhuttl told Bild the 23-year-old would be an outstanding addition.
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The 50-year-old leaves the Bundesliga club after finishing sixth in the club's second season in Germany's top tier.
Naby Keita is hoping to sign off in style at RB Leipzig as the future Liverpool midfielder will play his last Bundesliga game on Saturday.
Lookman struck twice in the 4-1 win over Wolfsburg, and the 20-year-old has played in 10 matches, scoring four goals.
Naby Keita received his fourth red card of the season as RB Leipzig's limp finish to the season continued with a 3-0 loss at Mainz.
Punishment means midfielder's season is over, with agent Hasan Cetinkaya calling it "an attack" on his client and the club.
Emil Forsberg fuelled rumours he could have already played his last match for RB Leipzig after simply writing "thanks for everything" on Twitter.
With Leipzig's hopes of securing a Champions League spot hanging in the balance, Naby Keita is set to miss crucial game against Hoffenheim.
Lookman, 20, joined Leipzig on a six-month deal without an option to make the transfer permanent in January.
A French TV football commentator was suspended Friday for anti-gay remarks directed at RB Leipzig players following a loss to Marseille.
Marseille stunned RB Leipzig 4-2 in a thrilling Europa League quarterfinal second leg on Thursday evening to secure a 5-3 aggregate victory.
Dayot Upamecano to Man United and Yaya Toure to Fenerbahce are two of today's transfer rumours, courtesy of Football Whispers.
Reported Manchester United target Dayot Upamecano says he dreamed of playing for the Premier League club, as well as Real Madrid and Barcelona.
Timo Werner pounced in first-half injury time as RB Leipzig edged the first leg of their quarter-final against Marseille.
Hasenhuttl, 50, has been linked with Bayern Munich and Borussia Dortmund in recent days.
Liverpool-bound Leipzig midfielder Naby Keita has to pay a fine of €250,000 on appeal for submitting false driving licenses to authorities.
Both the Blues and Atletico are considering goalkeeping options for next season should Thibaut Courtois or Jan Oblak depart in the summer.
Naby Keita, RB Leipzig's Liverpool-bound midfielder, pulled out of the Guinea squad with a lower back injury and the flu.