Alaba joined Madrid on a free transfer following a decorated spell with Bayern Munich, during which time he won an incredible 27 trophies.
The Austria international was presented to the media in the Spanish capital on Wednesday, where it was revealed he would inherit the number four shirt from Sergio Ramos, who has joined Paris Saint-Germain following a career-defining association with Los Blancos.
That in itself was a point of intrigue, but Alaba also addressed Varane – who he hopes does not follow the veteran Spain centre-back out of the Santiago Bernabeu exit door.
"I would have loved to play with Ramos, of course," he told reporters. "He is a leader, it would have been a pleasure.
"Varane, of course I would like to play with him. He is a player who has played excellent football.
"He is a great defender and has very good qualities. "
Alaba explained he has spoken to Ramos about taking on his famous shirt number.
"Ramos was here for a decade and has played football very well wearing this number and has become a leader," he said. "It is something that is present in everyone's head.
"He spoke to me. I was told that it is the last available number and I did not want to ask other players for their number. I feel honoured and it is a great motivation for me."
Even though a tough close-season market and the relatively parlous state of Madrid's finances look like obvious stumbling blocks, Paris Saint-Germain superstar Kylian Mbappe continues to be linked with the club.
Alaba was on the winning side when Bayern beat PSG in the 2020 Champions League final, but Mbappe excelled when the Ligue 1 giants deposed the European champions in last season's quarter-finals.
The France forward's 42 goals in all competitions last season put him second only to Robert Lewandowski (48) across Europe's big five leagues.
"He is a world-class player and he has enormous quality, that is something indisputable," Alaba added.
"I think it is something that does not affect me. That question should be addressed to other people."