Ronaldo played under Rangnick last season when the German took over at Old Trafford as interim manager at the end of November last year.
It was not a great time for the Red Devils as Rangnick struggled to get his ideas across and United ended up finishing sixth, 13 points off the Champions League places.
Ronaldo continued to get in the United team under Rangnick, memorably scoring hat-tricks against Tottenham and Norwich in the Premier League.
However, the Sunday Times reports that Rangnick could not recommend the Portuguese veteran to his compatriot in charge of Chelsea, in fact he advised Tuchel not to sign Ronaldo.
The 37-year-old has been pushing for a move away from Old Trafford this summer, wanting to play in the Champions League as he nears the end of his career at the top level, and Chelsea were mooted as a possible destination.
New Blues owner Todd Boehly was reportedly keen to bring in Ronaldo as a statement signing and a replacement for outgoing Romelu Lukaku, but Rangnick’s words with Tuchel put an end to the possible deal.
Ronaldo is still looking for a club to make Manchester United an offer for his services, but none have stepped forward yet.
The veteran has played in all four of United’s games so far this season, but only started one and was left on the bench for the last two matches, which the Red Devils won, making Ronaldo’s return to the starting XI looking unlikely in the near futur