Quilt running man:
Monopoly running man:
Well, I can definitely see a resemblance there! Googling "nursery rhyme running man" leads to Wee Willie Winkie:
Yeah, not so much. That google search also leads to The Gingerbread Man, which I think we can safely rule out here.
Googling "children's book running man" leads to about a million entries for Stephen King's novel The Running Man, which ... would make for an entirely DIFFERENT type of quilt, yikes.
So! I'm not sure if we're making a lot of progress, here, but it sure is interesting!
UPDATE: James P. brought up "Tom, Tom, the Piper's Son" in the comments, so a quick google search led to this:
Also a possibility!