Arroyo was cut by the team Tuesday, in a move that is expected to clear a roster spot for the incoming Bibby.
Players were told of the Arroyo move on Tuesday. Arroyo was not at practice and the team said Heat President Pat Riley would make a statement about his status later in the day.
Heat forward LeBron James says the team will welcome Bibby "with open arms" once his signing becomes official.
Bibby was traded by Atlanta to Washington last week. The Wizards and Bibby reached a buyout agreement on Monday, and Bibby could be in uniform for the Heat as early as Thursday night's game against Orlando.
He has to clear waivers before being signed to a team.
The Heat's other potential late-season addition doesn't appear he will be coming to South Beach.
Forward Troy Murphy reportedly has signed with the Boston Celtics and will be a potential thorn in Miami's side come playoff time.