Madrid boss Ancelotti has been strongly linked with the job, despite still having another year to run on his contract at the Santiago Bernabeu.
Rodrygo is one of three Madrid players in the Brazil squad, along with Eder Militao and Vinicius Junior, and he would welcome the appointment of Ancelotti as Tite's successor.
"We joke with him: 'Wow, coach, we're waiting for you there'," Rodrygo told Globo. "He jokes that we'll make the squad list together, the four of us in the same room.
"We talk in a joking tone, but every joke has a bit of truth. The situation is difficult because it means he'd have to leave Madrid.
"That way I can't say anything beforehand, but of course it would be an honour to have him here."
The Brazilian Football Confederation last month denied an agreement had been reached with Ancelotti to replace Tite, who left after Brazil's World Cup quarter-final elimination to Croatia.
Ancelotti has won 25 trophies across his 28-year managerial career, including four Champions League titles – two with Milan and two in separate spells with Madrid.
Speaking earlier this week, goalkeeper Ederson suggested "there is a big possibility" Ancelotti will take charge of the five-time world champions.
"Just look at his CV. We will know shortly whether he will be here or not," Ederson said. "I hope we can have a new coach quickly.
"I feel the anticipation too because there's too much speculation. Is it a Brazilian or a foreign coach? We are also living that phase of anxiety."
Under-20 coach Ramon Menezes will oversee Brazil's friendly with Morocco in Tangier on Saturday.