The veteran Brazil midfielder has announced this will be his last season with Manchester United.
Former club Sao Paulo had hoped to tempt Casemiro home after this summer's World Cup, but the midfielder has other ideas.
Rui Costa revealed: "We were one afternoon talking about it and one of our important players sent a message to Casemiro.
"Who wouldn’t like to have Casemiro in their team, right? I would.
"He immediately replied saying that his project was not to return to Brazil, that his project was to remain in another market."
He added,"Does that mean Sao Paulo made a proposal for Casemiro? No.
"Sao Paulo did not make a proposal for Casemiro and it would not, in my view, be prudent to do so without having a clear picture of how our squad would look. There was no proposal, there was no formal enquiry. It was through an important person in the group who sent him a message."