How would I go about taming a stray cat I see outside my apartment?

I live in a city and the building next to mine is abandoned. If someone does own it, ive never seen the owners.

Regardless, I have seen stray cat outside sometimes. He just lays on the sidewalk on his stomach and looks around curiously/alert. If you go within like 15 feet of him he runs between the buildings (maybe 10 inches/25 cm of space). I bought some cat food and a couple little bowls and i left food and water out for him. I made sure he saw me poor it and then i left the bowls an arms length deep into the opening. He just sat and watched me.

I went for a walk and when i came back he was eating. The second he saw me he kinda ran away. A lil later he ate again and i sat about 10 feet away just so hopefully he can see im non threatening?

Anyway, what could I do to get him to trust me safely? I live in Chicago and theres a lot of rats and stuff, I dont wanna get sick or bring anything to my sisters dogs etc. I also dont know if i should just befriend it and then let it stay outside or try and adopt him and being him inside. It gets very cold in chicago winter i want him safe!

I dont know much about cats as Ive always had dogs. Idk what to look for in terms of good/bad signs or what I should try to do. Thank you guys!

Edit: im wondering more about the catching process than anything

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from Pets https://www.reddit.com/r/Pets/comments/qlhl4r/how_would_i_go_about_taming_a_stray_cat_i_see/