Rangnick is expected to be confirmed as United's stand-in manager for the next six months before a permanent appointment is made next summer.
The Red Devils are seeking a replacement for Ole Gunnar Solskjaer, who was sacked after last weekend's 4-1 defeat at Watford.
United have reached an agreement with Locomotiv Moscow, where Rangnick currently works as a director, for the 63-year-old’s imminent appointment.
Tuchel once played under Rangnick at Ulm in the German third tier. The former Leipzig boss also played a key role in Tuchel’s move into management.
"He helped me a lot because he was my coach and then one of the main figures to convince me to try coaching," Tuchel responded to reporters at Friday's pre-match news conference.
"He was a huge influence on all of us at this time because he showed us it's not important to follow people to the toilet in games.
"That was the belief in these days that the defenders follow their strikers wherever they go and he showed us that it is possible to defend everybody in a zone.
"But listen, before I get carried away and talk too much, he isn't appointed yet. So let's respect everybody, let's respect Ralf and the club's decision.
"When things are done then we can maybe talk about it."
