Suarez, 25, has struggled to cement his place at Barca since returning to the club in 2016, spending the second half of last season on loan at Arsenal.
The former Villarreal midfielder, who battled a groin injury to finish 2018-19, has confirmed his desire to leave the LaLiga champions.
"What I want is to leave Barca and play," Suarez told El Larguero.
"My goal is to stay in the Spanish league. I have been in Barcelona for two months recovering from the injury and nobody from Barca has told me anything."
Suarez, who is contracted at Camp Nou until 2021, has been linked with a move to Valencia.
The one-time Spain international is seemingly interested in a reunion with Marcelino, who was his coach at Villarreal and is now at the helm of Valencia.
"Marcelino is the best coach I've ever had. I speak regularly with him," Suarez said.
"It's not true that I rejected Valencia. Valencia have never shown any interest in signing me as they are doing now."