Valverde has led Barca to back-to-back league titles in his two seasons in charge, but has thrown away two three-goal advantages in back-to-back Champions League campaigns to Roma and Liverpool.
The former Athletic Bilbao boss is under growing pressure, following the Copa del Rey final defeat by Valencia.
And Guardiola, who previously managed Barca between 2008 and 2012, has been mooted as a possible replacement.
However, the City manager has ruled himself out of the running, urging the Nou Camp board to stick with his friend.
“Valverde seems spectacular beyond the great friendship that unites us.
“He has done a very good job. It is true that he has lost in the Champions League, but we all lose.
“A team that wins two consecutive leagues and makes good football, I celebrate that it continues. Barcelona is still true to its style,” Guardiola said according to the UK Metro.
