The 24-year-old is the tournament's joint top goalscorer going into Sunday's final against Paraguay, having scored two of his three goals in Uruguay's semi-final showdown against Peru.
"We're all absolutely delighted for Luis," he told the club's official website. "He has done really well over there. He's taken his goals well and showed what a big threat he is.
"It's a fantastic achievement for him to get to the final of the Copa America and he has made a huge contribution to Uruguay's progress.
"We're looking forward to him winning the final and then coming back to us. Hopefully he will be back with a winners' medal."
The club have told both Suarez and Brazil's Lucas Leiva, who also took part in the competition, that neither man will be rushed back into Liverpool's preparation for the new season.