Caparros has been out of a job since January 2015, when he was relieved of his duties by struggling Granada, who were bottom of La Liga at the time of his departure.
The 60-year-old's best achievement came in guiding Villarreal and then Sevilla to promotion to the Spanish top flight in successive campaigns, as well as a moderately successful spell in charge of Athletic Bilbao.
Despite experiencing mixed fortunes in recent years, Caparros has been backed by the head of the Spanish FA, Angel Villar, to become Del Bosque's successor, whose contract expires at the end of Euro 2016.
Asked if he would like to become Spain coach, Caparros told Radio Marca: "Like every manager in our game, I would love to.
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"But I hope Del Bosque stays for many years. We have a special national team coach.
"If he extends his contract, it would be good for our game. If not, it would be an honour [to be coach], but we must all convince him to continue."
Spain were held to two stalemates in their most recent international friendlies, drawing 1-1 against Italy and then 0-0 with Romania, but Caparros was able to draw positives from the results.
"No one has beaten us," he said. "These friendly games only serve to work out other types of things."