De Gea and captain Iker Casillas are competing for the starting spot at the European Championship, where Spain face the Czech Republic, Turkey and Croatia.
Del Bosque's men complete their preparations for the showpiece tournament with a friendly against Georgia on Tuesday.
Speaking at his pre-match news conference, the 65-year-old said he was in no rush to make a decision before his side's opening game of the event on June 13.
"It's possible that De Gea will play tomorrow. Casillas did so against South Korea and that's all we can say," Del Bosque said.
"I don't have to make that decision now, and I'll make my mind up at a later date."
Del Bosque was unwilling to make guarantees over his team for the tournament opener, with Spain coming off a 6-1 thrashing of South Korea.
His focus is instead on the two-time defending champions become more familiar with one another.
"I don't know because our concern is that the 20 field players have a chance and become familiar," Del Bosque said.
"We know how we're going to play. The most important thing is to know how we play and tomorrow we will put it into practice."