López Caro has thrown his weight behind a move for Olise and described the Bayern Munich attacker as an ideal complement to the club's existing attacking talent.
Speaking on El Programa de Ortega on Radio MARCA, López Caro was asked whether he would recommend Florentino Pérez make a major investment in the French international.
"Without any doubt," he said. "I love that player. Not just for his qualities, but because he is very competitive and very ambitious."
The prospect of Olise lining up alongside Vinícius Júnior and Mbappé clearly appeals to the former coach.
"Imagine Olise, Vinicius and Mbappé together up front," López Caro said. "I don't need to say anything more."
He was also quick to note that ability alone is not sufficient for the demands of the Bernabéu.
"To be a Real Madrid player you don't just have to be a good player or an excellent player — you have to have a very ambitious mentality. Being the number one in every match is not easy. Maintaining that mental strength and the equilibrium that Madrid's players need is very difficult. And many players, however good they are, simply don't make it."
Olise, 24, had an outstanding debut season in the Bundesliga following his €50 million move from Crystal Palace last summer, and his performances at the World Cup for France have kept his name at the top of several clubs' lists.
Real Madrid have publicly denied any contact with Olise's camp, though reports linking him with a move to the Bernabéu have persisted throughout the tournament.