Valverde signed a two-year contract with Barcelona upon his arrival in the summer of 2017, and although the deal involves the option of a 12-month extension, neither party has made a move to trigger the clause.
The manager led the Catalan giants to a La Liga and Copa del Rey double last term, but Segura has confirmed that a decision on the Spaniard's future has not yet been made.
"Ernesto Valverde? He is on a two-year deal and there is an option to add a third, we will come to a decision which suits both parties," Segura told Sport.
Barcelona have only won one of their last five matches in all competitions and have been victorious in just one of their last four La Liga fixtures.
Valverde's team will welcome top-of-the-table Sevilla to Camp Nou on October 20.