The Spaniard, the 18-year-old son of rally legend Carlos Sainz, is in pole position to drive for Red Bull's second team Toro Rosso in July's young driver test at Silverstone.
Marca sports newspaper said Sainz's debut has not been officially decided or announced.
Speed Week said Portuguese younger da Costa is the favourite to drive the championship-leading Red Bull RB9 at Silverstone.
Sainz Jr will begin his GP3 campaign this weekend in Barcelona, driving for the team co-owned by Red Bull driver Mark Webber and his team boss Christian Horner.
"If I do well this year it's a step forward," he is quoted by Marca, "but right now F1 is not the first goal.
"First I need to do well here (GP3), then there are other steps, like the (Renault) world series."