Rangnick was appointed Manchester United's interim manager in late November on a deal until the end of the season after Ole Gunnar Solskjaer was sacked.
The German tactician has failed to really convince in his seven games in charge of the Red Devils, who are still outside the Premier League top four.
Man United will look to appoint a full-time manager this summer and Scholes has pinpointed Tottenham Hotspurs boss Antonio Conte as his preferred choice.
“We have gone to a man well regarded across Europe, especially by managers who speak highly of him like [Jurgen] Klopp and [Thomas] Tuchel," Scholes said of the German tactician on the Webby and O’Neill YouTube channel.
"But he’s not had much success as a coach.
“He won promotion in Germany and a bit with Schalke but he has been asked to come and manage the biggest club in the world - it's something I just cannot get my head round.
“They should have the best available out there as their manager. They haven’t got that and I find that astonishing.
“We should have one of the top five managers in the world. Now, Tuchel, [Pep] Guardiola and Klopp are the top three but they are unavailable, there is no chance of getting them. But then you look at Antonio Conte."
"Some people say he was not suited to United but you have seen what he is doing at Tottenham with a squad that is nowhere near as good as United’s," he added.
“He will probably challenge for the top four and United missed a trick with him. They could probably still get him from Tottenham. Tottenham fans probably won’t like me for saying that.
“You can see he is already getting frustrated with his squad of players and is asking for other stuff. Conte could do something special here, he has got the pedigree to do it. Will we be able to get him? I don’t know.”
