The Bundesliga outfit sacked Domenico Tedesco after a 4-1 thumping at home to Shakhtar Donetsk on Tuesday night with former Parkhead attacker Maryan Shved netting a brace,
Leipzig currently sit 12th in the German top-flight after a poor start to the season.
Popular German newspaper Bild have revealed is to be appointed this week as the media outlet detailed the reasons behind Tedesco’s sackings.
As per commentator Derek Rae, comments made by the Italian-born boss ahead of the Europa League semi-final didn’t impress club CEO Oliver Mintzlaff.
He had said: “Even if we now lose everything it will still be a super season for us.”
Leipzig lost to Rangers but finished fourth in the Bundesliga. The loss to the Ibrox side still hurts the German side with Bild referring to “limited Rangers”.
Rose is familiar to Celtic having managed Red Bull Salzburg between 2017 and 2019. The club's met in the Europa League with the Austrians winning both games. His success with Salzburg in the Red Bull stable prompted a move to Borussia Monchengladbach then Borussia Dortmund who he will face this weekend.
He lost to Rangers in the Europa League as Dortmund boss.
The 45-year-old, who was once manager of Lokomotive Leipzig, was linked with the Celtic job when the club were on the hunt for a permanent replacement to Brendan Rodgers. He would eventually take over at Monchengladbach.
Celtic will face RB Leipzig in the Champions League group stage twice in October with the second match at Celtic Park.