Both minky and fleece are synthetic fibers. I don't think they will absorb water well. Flannel might work. But, honestly, I'd try the bamboo that Krisb mentioned first.
Here are two links to bamboo wash cloths:
https://www.amazon.com/Natural-Organ...ustomerReviews
https://www.amazon.com/Motherhood-Co...dp/B011J9BYC8/
And here is a link to bamboo towels:
https://www.amazon.com/Taprilt-Extre...dp/B01H95SCPI/