The 25-year-old, who was born in Brazil, was widely expected to lead the line for Spain in the tournament, which gets underway next month.
However, a hamstring injury, which the forward aggravated in the 1-1 draw with Barcelona at the weekend, has placed his involvement in major doubt.
It is widely understood that the strain will keep him out of the Champions League final against Real Madrid this weekend.
However, according to reports in Spain, his World Cup position is also in severe doubt.
La Roja will travel to their pre-tournament training camp in the United States in two weeks.