The 21-year-old put in an excellent display in his side's surprise win over Uruguay on Saturday as he scored his side's first goal and set up the third.
Wanchope revealed that Campbell is now desperate to force his way into the Gunners squad next season, after spending the last campaign on loan at Olympiacos.
"He really wants to go back to Arsenal and play, and I told him that the only way to do that is on the pitch," Wanchope is quoted as saying by The Mirror.
"He did well against Uruguay and I think that he needs to perform even better against Italy and then England to have that chance to go back to Arsenal. I'm sure that Arsene Wenger will have a look at him.
"He will improve. You saw the game. He is capable to play up front or on the sides so he will do well."
Costa Rica face Italy in their next Group D match on Thursday.