Lopetegui was named as Zinedine Zidane's successor at the European champions in a surprise announcement on Tuesday.
Del Bosque, who managed both Madrid and Spain, feels former Porto coach Lopetegui will not let the announcement hinder his side in Russia this summer.
"I am convinced that Lopetegui will do the same role, it will not affect him," he told Onda Cero .
The 67-year-old was also pleased that Madrid turned to another Spanish manager, and believes the 51-year-old is ready to take the helm for Los Blancos.
He added: "I always lean towards the Spanish coaches. I think Lopetegui is ready to train Real Madrid."