Estadio Deportivo and Radio Marca report the Costa Rican international is set to complete his medical at Los Verdiblancos this evening.
The 25-year-old previously enjoyed a loan spell at the Seville-based club in the 2012/13 season, netting twice in 21 La Liga starts.
Campbell has since enjoyed loan spells at Olympiakos, Villarreal and Sporting CP, while also enjoying first-team action at the Gunners, and is said to be open to a move.
Despite suffering an injury on international duty in the Gold Cup in June but is expected to return to first-team training next week.
Betis earlier announced the departure of midfielder Didier Digard while Darko Brasanac has joined Leganes on loan and Roman Zozulya is expected to depart.