The Madrid veteran, 34, said he has had many offers, including some from clubs in England but Paris Saint-Germain are the current favourites.
According to a report in Marca, Pepe was ready to sign for Inter Milan, before PSG boss Unai Emery hijacked the deal.
The Portuguese defender has also rejected a big-money offer from Chinese club Hebei Fortune.
Speaking to Spanish radio station Cope, Pepe also took a parting shot at Madrid coach Zinedine Zidane: “I don't want to blame anyone. What Zidane has done with Real Madrid is spectacular, but there are things I don't understand.
“I didn't say goodbye to Zidane, because Zidane and Real Madrid knew I was going before I did.”
Pepe has made 334 appearances for Madrid since his £25.5 million move from Porto in 2007, but has fallen out of favour under Zidane, with Raphael Varane and Nacho preferred.
His contract runs out this summer.
“It is clear that I will not continue at Real Madrid,” he said.
“One stage is over and, from now on, another one will start. There are more offers, also from England.”
Pepe was born and raised in Brazil before moving to Europe at the age of 18.
He has won three La Liga titles, three Champions Leagues, two Copa del Reys and two Club World Cups during his time with the Spanish giants. He was also part of the Portugal team that won Euro 2016.