Messi remains sidelined after suffering a right ankle injury a month ago in Argentina's 1-0 victory over Colombia in the Copa America final.
Messi has not yet trained with his Miami teammates since escaping a walking boot.
The Leagues Cup is a tournament with MLS and Liga MX Mexican clubs, with Messi helping lift Miami to last year's inaugural title.
The showdown match between the Columbus Crew, last year's MLS kings, and Miami, this year's top overall team in the league table, is among eight matches that will decide quarter-final pairings on Friday and Saturday.
In Monday's round-of-16 opener, the host Seattle Sounders beat Mexican side Pumas 4-0.
Paul Rothrock's header off a centering pass from Albert Rusnak in the 32nd minute gave Seattle a 1-0 lead and Jordan Morris doubled the Sounders' edge in the 58th with Rusnak again on the assist.
Slovakian Rusnak scored on a penalty shot in the 71st minute and Morris added a final goal from the spot in the fifth minute of stoppage time.
Seattle, which also defeated Pumas in the 2022 CONCACAF Champions League final, will next host the winner of a Tuesday match between San Jose and Los Angeles FC.
Other knockout matches on Tuesday include Philadelphia at Cincinnati, Cruz Azul against Mazatlan, Tigres against New York City, Toluca at Colorado and Club America at St. Louis.
