But the young replacement from Udinese thinks the pair would work well in tandem.
"It would be beautiful," Parks told La Nacion newspaper from the team's training base in Suzuka. "We understand each other very well and could do a lot of harm."
Parks, 20, scored for Costa Rica in a friendly against Japanese club Honda last weekend.
However, coach Alexandre Guimaraes seems reluctant to start World Cup matches with both strikers, preferring to see them as alternative attacking options.
"The good thing is that I have a lot of alternatives to choose from," Guimaraes said. "If the other team has a strong defence, I have forwards to counter that."
One of his assistants, Rodrigo Kenton, said that the possibility of lining up Parks and Wanchope side by side has already been discussed among the Costa Rican coaching staff.
However, Parks said that he is willing to follow Guimaraes' orders, even if that means that he will only get to play when Wanchope is injured.
"We have a system that provides for me and Wanchope to play together, but the coach hasn't said anything about it," Parks said.
"We've been practising our usual system with only one forward deep inside the other team's defence."
Parks said that he has been learning a lot from 25-year-old Wanchope, who has been playing in England for the past five years.