According to The Sun, the comic approached the man, known locally as 'Thomas', after attending a yoga session in a nearby street.
"This guy Thomas was in a bad way," a witness told the paper. "He'd been lying on the floor and talking to himself.
"On leaving the studio in his car, Russell noticed him there and was parked and out of the vehicle in no time to help. He asked the guy his name and what was wrong.
"I heard him offer to take him for some food. Thomas said he wanted a burger, to which Russell replied, 'You don't want any of that cr*p, come to my house and you can have some proper food and a nice bath'."
Brand is due to return in a second series of his topical US talkshow Brand X later this year. He has described the new season of the FX programme as "a bit more normal" than the first.
Watch a promo for Brand X below: