Costa, 24, is eligible to represent Spain despite appearing in two friendlies for Brazil, the country of his birth, earlier this year.
Del Bosque confirmed on Monday that the Spanish Football Federation had written to FIFA to request the official paperwork, with the Spanish boss admitting that the powerful forward would offer him a "different" option in attack.
"To consider Diego Costa is a sporting decision. It has still not been confirmed that we can call him," Del Bosque told Tiki-Taka.
"He is playing well and is one of the architects of Atletico Madrid's great moment. He is a different player.
"I have seen that he is also not used only as a centre-forward, one week he played out on the wing... at Atletico he has played in various positions and almost never as a centre-forward."
Costa has scored eight times in La Liga this season.