Rodrigues said he would also approach the Spanish club's president Florentino Perez and described Ancelotti as their first choice to replace Tite, who left the Brazil team after their quarter-final exit at the World Cup in Qatar in November.
"He remains the Plan A and in this trip with the selection in Europe we can have greater clarity," Rodrigues said on Tuesday in a press event at CBF headquarters in Rio de Janeiro.
Brazil will play Guinea in Spain on June 17th and Senegal in Lisbon, Portugal on the 20th.
"The trip will be very significant for us (to decide the future coach). I intend to talk to Ancelotti and the president of Real Madrid. Only after that will it be possible to say if it will happen or not," Rodrigues added.
The Italian coach has a contract with Madrid until 2024 with a termination penalty in the agreement. According to Rodrigues, this should not hinder any possible deal with Brazil.
"The issue, for sure, is not the fine. The problem is the contract and nobody wants to break it," he said.
"We are invested in this idea and we are doing everything in our power to make it work and become a reality."
Last month, Ancelotti dismissed Brazil's interest by saying he would honour the last year of his contract with Real Madrid.
The Brazilian national team have been without a coach since their World Cup exit and lost their first friendly of the year 2-1 to Morocco in March, led on an interim basis by U20 coach Ramon Menezes, who will be back for the friendly matches on European soil this month.
