Only an 11th-hour appeal would give the Barcelona forward any hope of appearing for the defending champions in Chile next year, after his eight-match international ban for biting at the World Cup.
While Valdez revealed talks were ongoing with the Uruguayan body and FIFA, he was realistic about the chances of their star man appearing at the continental competition.
"We are still negotiating this issue with FIFA, but we almost have ran out of options, and the truth is that it will be a miracle if Luis can play at the Copa America," Valdez said.
"So far we have been on the Saudi [Arabia] tour that we did in October, which we used to speak with Luis about his return to the national team after the World Cup.
"We said a lot of things with him, but we think that's in the past.
"Obviously, Luis knows that he made make some mistakes, but anyway we still feel that some FIFA decisions during the World Cup, weren't right.
"But that is in the past, now we must focus in the present and on the future ahead."
Uruguay have not lost in 90 minutes in their six matches since their exit in the last 16 of the World Cup, with the South Americans' only defeat coming in a penalty shoot-out to Costa Rica after their friendly ended 3-3.
They have beaten Japan, South Korea, Oman and Copa America hosts Chile, while drawing with Saudi Arabia.
Valdez said despite the positive results, Oscar Tabarez's men are continuing to rebuild.
"The team is okay. We are in a rebuilding phase," Valdez said.
"As you know, in the last few friendlies matches, including the last one here in Santiago - a very rough game against Chile, we use some experienced players but tried also some new younger ones that are showing promise.
"And of course, we are going to miss Luis Suarez, because he is a world class player.
"But we have belief in the national team and the process that has been going on for a few years in Uruguay."