Vettel announced his retirement on Thursday and has 10 races remaining before he leaves F1.
The news means there is a vacant seat alongside Lance Stroll at Aston Martin next year, and speculation is rife over who will fill it.
Vettel, who is close to the Schumacher family and grew up idolising Mick's father, Michael, said he had briefly talked to Aston Martin owner Lawrence Stroll about possible replacements.
"Well obviously I spoke to Lawrence and told them that I am not going to continue," Vettel said. "We did have a very, very brief chat about what might be next.
"I do have my opinion. I think very highly of Mick. I'm obviously not entirely objective because I am very close to him, but I do think he's a great driver.
"He's a learner, he keeps learning when others sort of stall or stop making progress. So he does have a lot of qualities, but he is also very young still.
"So I don't know. It's not my decision. If I am asked I will give my opinion, but in the end the team have to make that decision."
Schumacher currently drives for Haas but is not contracted to the team beyond the end of this year. Haas team principal Guenther Steiner said Vettel's decision to leave Aston "doesn't change anything for us" and said he and team owner Gene Haas would make a decision by the Italian Grand Prix in September.
"We will know by the end of the European season what we are doing, and then we will communicate it," Steiner said. "We need to start to speak to Gene about it and talk through the different scenarios of what we are going to do.
"It has become standard to speak about this, but we will take our time."