Pedro told Ser Catalunya this week that he would love to go back to the club where he won 20 major trophies, including five LaLiga titles and three Champions Leagues, between 2008 and 2015.
The 32-year-old has only played four times in the Premier League under Frank Lampard this season and, with his contract expiring at the end of the season, it has been suggested the Spain international could be allowed to leave next month.
Speaking to reporters on Friday, Barca coach Valverde said of Pedro: "He's an historic Barca player - let's not kid ourselves. He's one of the players to win the most titles with this club, but he plays for another club now.
"We have to respect players at other clubs. We'll see what might happen in the future."