"Regarding Barcelona's supposed interest, I don't usually talk about other teams and I won't start doing so now".
The pair have previous together, with the Spaniard playing under Valverde for one season at Bilbao before joining United in 2014.
"The coach, accompanied by president Josu Urrutia, will hold a press conference on Wednesday, May 24 at 1200 (local time) at San Mames", a brief club statement read.
53-year-old Valverde has managed the likes of Espanyol, Olympiacos, Villarreal and Valencia, winning six trophies in the process - including the Supercopa de Espana after beating Barcelona in the final in 2015. I first want to say goodbye to Athletic and then I will think of my future.
Valverde is widely reported to be the frontrunner for the forthcoming vacancy at Barca.
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The Catalans are on the hunt for a new boss with current manager Luis Enrique to vacate the hot seat after Sunday's Copa del Rey final, where Barca will face Alaves.
Spanish publication Sport claim the former Athletic Bilbao boss is a big admirer of the midfielder and believes he can make a difference at Barca. When I first came here I thought I would only remain for two years.
"I don't know what is being published but I am responsible for my own honesty".
However, Mourinho is in no mood to lose one of his best players this season and has demanded Manchester United offer the midfielder a new and lucrative contract in the summer.