Reports in France say the offer has been accepted by Rennes and medical already completed.
Camavinga 18-year-old French midfielder has a year left on his contract and the Ligue 1 side would prefer to sell him this summer to avoid losing him for nothing next year when his deal runs out.
Camavinga has been linked with Real Madrid, who are yet to spend big in the transfer market since the coronavirus pandemic hit the world.
Camavinga was also linked with a move to the Premier League club with Manchester United this summer, but journalist Fabrizio Romano announced that Camavinga is close to a move to LaLiga giants Real Madrid.
“Official bid from Real Madrid for Eduardo Camavinga: a bit more than €30m, add ons included in the proposal. Camavinga prefers to leave Rennes now more than a free agent in 2022. Agreement close to being finalized. #RealMadrid Personal terms agreed until June 2026.”
Having starred in Ligue 1 for Rennes, 18-year-old Camavinga was seen as an ideal target for United.
Camavinga was also tracked by Paris Saint-Germain (PSG), but now looks set to join Los Blancos.
The Rennes midfielder has reportedly agreed on personal terms on a five-year contract with Real Madrid.
Real Madrid have reportedly moved on from PSG striker Kylian Mbappe after making a €170 million offer, with another €10 million in potential add ons.