"We had a very similar situation, if I remember, with Jadon six or seven weeks ago,” Rangnick said,
"He is the best example of what can happen, again it’s the player himself who has to perform and get the best out of his own performance – and this is the same with Marcus."
Sancho initially failed to make an impact following his high-profile £73million transfer from Borussia Dortmund.
But after a rocky start, the 21-year-old winger is now beginning to find his feet in Rangnick’s side, with two goals and two assists coming in his last six games.
Sancho’s form has been in stark contrast to Rashford, who was hauled off in the 75th minute for Anthony Elanga against Atletico Madrid on Wednesday.
Elanga went on to score the all-important equaliser in the 1-1 draw in Spain, but Rangnick rejects the idea that there is anything hampering Rashford.
"He is definitely not injured. He definitely has no issues with his shoulder any more,” he explained on Friday.
"We have spoken a lot about Marcus in the last couple of weeks and I have personally spoken a lot with him.
"It's with him like with all the other players, when it counts and they are on the pitch, they just have to perform and I am pretty sure he is not happy with his performances right now.
"Right now he is trying to find his best possible shape and performance, and we just try to give him helping hands with everything we can. We show him video footage and we speak with him regularly.
"In training he is in top form. That is why I decided to play him (in Madrid). Now it’s about having that transformation from training performance to the competition in the league – and this is the next step he has to take."