However, the meeting quickly broke down when Valencia chief Rafael Salom demanded that Albelda sign a document which would mean he could not commit to clubs of the stature of Barcelona, Real Madrid, Villarreal and Atletico Madrid.
Albelda is insistent on being allowed to choose his next destination, particularly after the way he has been treated since the arrival of coach Ronald Koeman.
Valencia are desperate to avoid the case going to court and more talks are scheduled for Friday.