The 20-year-old Costa Rican was sent on a season-long loan spell with the La Liga side after his application for a work permit was turned down and has so far scored twice in 15.
Betis are currently eighth in the table and the youngster is hoping to help his temporary side qualify for Europe which could intensify his inclinations to stay at the Seville-based club.
"Being in a country like Spain and to play in this league means a lot. I want to keep playing well to keep progressing as a player," Campbell told Spanish paper Diario de Sevilla.
"I will concentrate until June and see what will happen after. I'll give everything on the pitch until June, until we reach that date, to see what happens with me.
"Arsenal are in charge of my career and I am longing to play with them, but I'm very comfortable here and I play for Betis wholeheartedly.
"I'm trying to give my all for Betis because they opened the doors for me. We can go ahead and we believe make Europe."