Del Bosque, who took over from the late Luis Aragones after Spain's triumph at Euro 2008, has previously suggested he will step down after the competition in France, where La Roja will be chasing an unprecedented third straight continental title.
Spanish media have reported that football federation (RFEF) president Angel Maria Villar is trying to persuade the 64-year-old to stay on until the 2018 World Cup in Russia and Del Bosque appeared to leave that possibility open in an interview with Spanish radio on Thursday.
"I think that in football matters you don't have to be very rigid," he told Cadena Cope when asked about his future.
Del Bosque is a hugely popular figure in Spain after leading the national team to a maiden World Cup victory in 2010 and a second consecutive European title two years later.
However, some felt that a fresh start was needed after Spain's failure to advance beyond the group stage at last year's World Cup finals in Brazil.
Among names to have been linked to the Spain job are Bayern Munich coach Pep Guardiola, Sevilla's Unai Emery and Rafa Benitez of Real Madrid.
Spain can make sure of their place at Euro 2016 with a win against Group C minnows Luxembourg in Logrono on Friday.
(Reporting by Iain Rogers, editing by Amlan Chakraborty)
