Boro are the only club to have had an offer accepted for the player, who is certain to leave Leeds this summer.
Negotiations are not expected to be straight forward, taking into account the complexity of Viduka's Leeds contract and in any case, he may prefer to keep his options open for the time being to see if there is still any interest abroad.
Juventus are among the clubs who have been linked, but Boro's is the only firm offer currently on the table.