The Barcelona full-back, who faced the same decision in 2006, has advised the Lagarto-born forward to think long and hard before turning his back on the Selecao
The Spanish Football Federation (RFEF) announced earlier this month that the Atletico Madrid striker, who was born in Lagarto but recently attained Spanish citizenship, has accepted an invitation to line out for la Roja.
However, Alves believes that the forward should think long and hard before following through on his decision to turn his back on the land of his birth.
"I would ask Diego Costa to make his decision with a cool head because he would also be an important player for Brazil," the 30-year-old is quoted as saying by AS. "It's not for nothing that he is the top scorer in La Liga.
"These decisions are very personal and you have to respect whatever Diego Costa decides.
"But, again, I would suggest he thinks coolly before making a decision he can't go back on.
"I have not spoken to Diego Costa about this decision because I do not want to interfere. Diego will know what is best for him.
"But, if in the end he decides to play with Spain, we will have to respect that.
"I, myself, went through this experience in 2006 when I was at Sevilla but I decided to play for my country."
Alves spent six seasons at the Ramon Sanchez Pizjuan before joining Barcelona in the summer of 2008.