The RB Leipzig forward has agreed a pre-contract deal to sign for the Blues in the summer.
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Nkunku is set to join the west London outfit in a deal worth more than £50million to strengthen their attacking options.
A Premier League move is now on the horizon, with the 25-year-old scoring 64 goals and assisting a further 52 across four seasons at Leipzig.
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However, Rangnick, who worked with Nkunku at the Bundesliga side, has expressed his concerns over the transfer due to Chelsea's situation.
With the Blues sitting 11th in the Premier League, he told ZDF sportstudio via BILD: "At the moment, no matter who comes as a coach, you can't really recommend anyone to go there.
"The very first thing to do is establish some sort of strategy and reduce the squad to a reasonable size that any coach can work with.
"I'm also thinking of a player whose commitment to RB Leipzig I was at least a little involved in - Christopher Nkunku.
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"For me one of the best attacking midfielders currently available. And who, in my opinion, decided to move to Chelsea far too early.
"Imagine he comes to a club that is in the state it is at the moment. Such an outstanding player. This hurts my heart personally. If I were his advisor or his father, I would be very worried right now."
Nkunku is set to be the next player to join Chelsea, who have spent close to £600million on new signings since last summer.
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Alongside their dismal league standing, Chelsea are also out of all cup competitions following their Champions League exit on Tuesday.
The Blues are searching for their next permanent managerial appointment, with Frank Lampard currently in charge as interim boss.
Mauricio Pochettino, Julien Nagelsmann, Vincent Kompany and a mystery fourth name are on a shortlist of options.