Lopetegui was dismissed Monday evening after just four months in his appointment as Zinedine Zidane’s successor.
He was sacked after Madrid were hammered 5-1 by Barcelona at the Nou Camp.
Lopetegui was “provisionally replaced” by ex-player and manager of Real Madrid Castilla, Santiago Solari.
But Rivaldo is now making a case for Pochettino to take over at the Santiago Bernabeu, stressing that he was the right manager to coach Madrid.
“From what I’ve been hearing, Florentino Pérez appreciates Mauricio Pochettino’s qualities and is interested in signing him,” Rivaldo told Betfair (via the Evening Standard).
“Pochettino is obviously a good manager with experience in La Liga and for that reason I believe he could be a good option for the club.
“Perez wasn’t expecting that things could go so wrong so quickly this season,” he added.
“Madrid’s poor start to the season might lead him to make a big investment in a new coach and maybe buy a new goalscorer to replace Cristiano Ronaldo.
“That’s where the possibility of bringing Pochettino, along with English striker Harry Kane, gets in the mix, but Real Madrid will need to invest seriously to achieve both, as Tottenham won’t be interested in losing them easily.
“I think both options could be important for Real Madrid. They are suffering up front, scoring very few goals and Kane could be the solution.”