Sure thing...a “saddle box” is what you want. It’s made so that the screws to mount the fan are in the wood. It’s the most secure mounting option for a ceiling fan.
https://www.amazon.com/dp/B000HEKU8G/ref=cm_sw_r_cp_api_glt_fabc_RC6JDH8G6GWVNT2W2S41
This is what I’m talking about for the ceiling fan.(probably cheaper at Lowe’s of H.D.)
That looks like a pancake box. They're not rated to support a ceiling fan as far as I know. And the fact that it's a pancake box probably means there is a joist or something there that would prevent the installation of a proper fan box in that exact location. There is a box made for going over a ceiling joist, if that's what is above this pancake box.
Here's an example of one if this sub allows links. There are several different kinds.
Edit: I looked again and the ceiling is built lower where that box is. Idk why they would have used a pancake box in this situation. So my ceiling joist theory is probably wrong in this scenario.
Can you shut off the electricity and remove the box to get a better picture? Just unscrew it and see what is underneath. I couldn't get your imgur link to load
The picture ended up loading. It's a pancake box and looks to be lag screwed into something.
I would personally remove the j-box and replace it with either a saddle box like this: https://www.amazon.com/Carlon-CFB-12-Ceiling-Saddle-Diameter/dp/B000HEKU8G/
or one like this: https://www.amazon.com/Westinghouse-0200011-Support-2-Cubic-Inch-Capacity/dp/B0002YV1Q6/
if for no other reason than to give you more room for tucking wires.
Carlon CFB-12 Ceiling Fan Box, Saddle, Round, New/Old Work, 4-Inch Diameter by 2-3/8-Inch Depth, Black https://www.amazon.com/dp/B000HEKU8G/ref=cm_sw_r_apan_i_2Y6S9MV0X8H3VHPCX4WK