The movie star and his mum share a passion for the reclusive British artist and when she was in London last year with Gyllenhaal's sister Maggie, she went out of her way to find Banksy.
The actor explains, "My sister was working in London and my mum babysits my niece a lot... but on her time where she wasn't, she went to go look for Banksy, because Banksy lives in London.
"It's very expensive to get a Banksy print, but she found out... that apparently Banksy puts out 350 prints every few months... and people can go online and try and get them for free.
"She went online before my birthday; 75,000 people got online to try and get 350 prints... and she got me a Banksy print. It was pretty amazing."