Liverpool and Real Madrid will contest the Champions League final in Paris on May 28.
Jurgen Klopp's men are chasing an unprecedented quadruple, having already won the League Cup and FA Cup and have been boosted by the winter arrival of Colombia international Luis Diaz from FC Porto.
Rodriguez has a close relationship with international teammate Diaz, and wants him to lift Europe's premier club competition at the expense of his former clubs.
On the back of an impressive FIFA World Cup in 2014, where he emerged as the goalking, Rodriguez joined Real Madrid, winning two La Liga titles and two Champions Leagues among other honours.
The 30-year-old, who now plays for Al-Rayyan in Qatar, spent two seasons on loan at Bayern Munich after losing his place at Real Madrid before joining Everton permanently in September 2020. He left the Toffees after just a season.
Speaking on his Twitch stream, James said: "Liverpool are going through a very good moment and have 'Luchito' Diaz there, I want Lucho to become champion.
"Madrid is very tough in this type of game. We've seen it in the quarter-finals and semi-finals.
"It's going to be tough. I have former team-mates at Real Madrid, I love the club very much, they have a long history in this type of game, but Liverpool can play a great game. I want Lucho to be champion."
Diaz has added renewed energy to the Liverpool frontline since arriving in January, scoring six goals and providing four assists in 24 appearances.
