FIFA launched proceedings against Uruguay's Jose Maria Gimenez (27), Diego Godin (36), Fernando Muslera (36) and Edinson Cavani (35) after the players angrily confronted the referee after they were knocked out of the World Cup despite beating Ghana in their final group match.
As a result, FIFA opened separate investigations against the four players and the AUF itself.
"We told him (Reck) when FIFA notified us and he immediately start to work," Gaston Tealdi, vice-president of the AUF, told Ovacion.
Reck, who has worked with the AUF before, also defended Argentina forward Lionel Messi (35) when he was given a three-match suspension for insulting a referee in a clash against Chile in 2017.
The lawyer got the ruling overturned and Messi was able to continue playing in the qualifiers for the 2018 World Cup.
"It's going to take a little while to know the sanction and even longer now that Uruguay are not in the World Cup. It could be a month, up to two months, even three," Tealdi added.
The AUF has 10 days to make a statement of defence as the penalties could range from warnings to economic sanctions and sporting fines.
