A disappointing 2018-19 season saw Madrid out of contention in La Liga, Champions League and Copa del Rey by March, leading to the return of Zinedine Zidane as coach -- which is likely to mean significant changes in the summer.
"I always say that Madrid must have the best players, as this is the best club in the world," Casemiro replied when asked about the potential arrivals of Pogba and Hazard. "But it is not for me to say which players should be signed.
"The president [Florentino Perez] and other people are very prepared for that. But they are both very good players, and very good players are always welcome at Real Madrid."
When asked if Pogba would be a good fit for the Madrid midfield, Casmiro added: "A world class player at his level can play in any team. If he comes to Madrid he would be welcomed very well -- we know he is a great player.
"For sure he is now thinking about his next Champions League game, that is type of person he is. We must respect Manchester United also."
Neymar is another player heavily linked with a move to Real Madrid and Casemiro said he would like to see his Brazil teammate move to the Bernabeu.
"[Neymar] is a great player, and it would be great if he came here," Casemiro said. "But this is a question for the president, and for Neymar himself.
"You'd have to ask him if he wants to come. He said recently he was happy in Paris, so we must respect him, and his club. But a great player like him would be automatic pick in any team."
Casemiro also dismissed suggestions he and his teammates were concerned new arrivals could see players leaving.
"Of course not," the 27-year-old said. "Those who have failed this year are the same as those who won three Champions Leagues in a row [2016-18].
"Great players are always welcome, but we have a great squad already, and we will win things again."
"At this club, we lose all together just like we win together," Casemiro added. "When one player is whistled, we are all whistled, we see things that way as a group.
"We should not talk about Marcelo's season, as we have all failed collectively. He is a great player and five months ago was named the best left back in the world.
"Bale has given this club many trophies, scored many goals. Maybe we have not had a good season, but we are all together in this."