It may be that this man is bringing communion to a friend, but doing so improperly.
Notify the priest. Be prepared to give the man’s name (if you know it) and his description.
The priest has two proper choices at that point:
Confront the man privately and instruct him.
Wait until he sees the man in the pew on Sunday, then give the congregation general catechetical instruction about the proper handling of the Holy Eucharist.
We had a situation like this, only we never did catch who at fault. What we were finding was hosts dropped on the floor between the water fountain and the wall. It appeared to be something a passive-aggressive rebellious teen would do: head for the water fountain after communion, hide the host, and return to the pew.
This happened for several weeks running. We informed Father, then he addressed the entire congregation about the scandal. He included instruction on the proper handling of a contaminated host. (The big potted plant by the altar had more than its share of “fertilizer.”) No names were mentioned, no fingers were pointed, but it stopped happening immediately.