Pepe, who was limited to just 18 appearances this season due to a number of injuries, is out of contract at Real Madrid this summer.
The 34-year-old won 13 honours during his time at the Bernabeu, including three La Liga titles and there Champions League crowns.
But the Portugal international, who played a key part in his nation's European Championship triumph last year, has confirmed he will end his 10-year stay at Real this summer.
Pepe has been heavily linked with Paris Saint-Germain and Inter Milan, but admits he has offers from the Premier League to consider.
"It is clear that I will not continue at Real Madrid," Pepe told Spanish radio station Cope.
Pepe confirms he will leave Real Madrid this summer
There are more offers, also from England
Real Madrid defender Pepe
"One stage is over and, from now on, another one will start. There are more offers, also from England."
Real manager Zinedine Zidane guided the Spanish giants to the Champions League and La Liga double this season.
And while Pepe does not blame Zidane, the experienced defender still has plenty of questions over his departure.
Pepe reportedly wanted a two-year extension in the Spanish capital, but Real were said to have only offered him another season.
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He added: "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."
Back in February Zidane urged Pepe to remain at the Bernabeu amid interest from the Chinese Super League.
"I would like him to stay, as long as he wants, of course," Zidane said.
"He remains an important member of the squad. But we will see in June. With all Pepe has done at this club, we must respect whatever happens with him."