As Souffle says, it's not safe. You may have seen that youtube video where someone uses fleece strips for bedding and thinks it's ok but it's too risky really. Torn up plain white toilet paper is best - and hams enjoy weaving the strips into their nest and making it cosy that way. I tear a sheet lengthwise into 5 or 6 strips and do that until you have a big mound of it to put somewhere in the cage. Hams will pouch anything that looks like food or nesting material. I think it's fun watching them pouch the toilet paper strips
The fleece could be nice to use for out of cage time when you're monitoring, but if the hamster starts to chew it then take it away again. As long as there are no frayed edges or loose strands. Our hammy had a fleece blanket he liked to curl up in on the sofa and he didn't try to chew that but anything like fluffier fleece or a hammock he would try and chew.