He continued: "There is a lot of speculation regarding my future but, I have to say it clearly, I haven't committed myself to any team".
However, his form has not gone unnoticed by his former boss Ernesto Valverde, who is expected to be named as the new manager of Barcelona on Monday.
When pressed further about the supposed interest from Barcelona, he added: "I'm not going to talk about specific teams now". He also coached the club from 2003-05.
He guided them to seventh in LaLiga this season having finished fourth, seventh and fifth in the previous three campaigns.
He previously coached Espanyol, Olympiakos, Villarreal and Valencia.
"I don't know what's been published", Valverde said. "The group spirit is what stays in my memory".
New Balance has been gently growing its portfolio of football clubs which includes Liverpool, Celtic, FC Porto, Sevilla, LOSC Lille, and national football teams, Costa Rica and Panama.
"I have told the players that this group will remain in the memory of the people". The outgoing Athletic Bilbao boss admitted his agent has been approached by some clubs, amid suggestions Arsenal are also tracking his situation.
"We have to thank him for his work in these four years", Urrutia said. "It doesn't depend on what Real Madrid do, I just think we can aspire to much more".