The trainer hints that the attacker may not be taken to Ukraine and Poland after an average season, and has backed Gerard Pique to cover for the injured Carles Puyol
The 24-year-old has struggled with injuries this term, preventing him from hitting his best form, and has failed to make an impact for club and country.
The Spaniard was not called up for his nation's last friendly, a 5-0 win over Venezuela in February, and Del Bosque says that there is not guarantee he will win his place back in time for the European Championship.
"Pedro has been trying his best," he told Sport. "But he's had an erratic season. We have a limit of 23 players, and we can't take any more."
Another doubt for the world and European champions is David Villa, who has been sidelined since December with a broken leg and Del Bosque hinted that he would take a cautious approach before selecting the striker.
"I'm concerned because we don't know what the situation is. The player is working hard, but haven't seen the signals from the player that we would like."
One Barcelona player who is definitely ruled out of the Euros is Carles Puyol, who succumbed to a knee injury this week. However, Del Bosque says that he is confident that Gerard Pique will be able to cover for his Blaugrana team-mate.
"We have great confidence in him, and he's an important player. In defence, we have many options. Javi Martinez can also play at the back or in midfield."
Spain kick off the Euro 2012 campaign game against Italy on June 10 before facing the Republic of Ireland and Croatia.