Perez said he would sign "both" Mbappe and Neymar after being asked who he would choose of the star forwards following Zinedine Zidane's return to Madrid on Monday.
Madrid have long been linked with Mbappe and Neymar and speculation over the duo has heightened after Zidane's comeback as the Frenchman looks to overhaul the La Liga giants.
"It's normal because everyone wants Neymar, Mbappe, [Marco] Verratti or Marquinhos on their team, it does not bother me to say that," Tuchel told reporters.
"They are top players but they are our players and it's the most important."
Mbappe, Angel Di Maria, Marquinhos and substitute Eric Maxim Choupo-Moting scored for the French champions away from home as the leaders stayed 17 points clear atop the table.
"I was waiting for that because the team made a good impression during the training," Tuchel said. "We talked a lot. I was very calm and convinced that we are able to show and start again.
"It was a good opportunity to play again together. Having talked a lot about this match against Manchester, the team did things well with a lot of good qualities, a good pace, we scored four goals, created a lot of opportunities.
"It was a first step to show that we could react like champions. It's a good reaction, we still have goals, we want to win competitions [which remain], the championship, the Coupe de France."