Messi was substituted in Inter's NBA match against Toronto before the break due to an unspecified injury and missed last Sunday's game against rivals Orlando City.
The Argentina captain is a doubt for the Copa America final, as his side seek their second title after winning the Mexican-American Cup last month.
Martino told a press conference on Tuesday: "We'll wait for Leo until tomorrow. Until the last minute. I will sit down with him to assess his condition. Maybe we will reach an agreement tomorrow."
"There are three sides here, the player, the final and then what comes next. We have to try to decide. There are always risks. But we have to reduce it."
Messi, a seven-time Ballon d'Or winner, has scored 7 goals and provided 11 assists in 5 appearances for Inter Miami since arriving from Paris Saint-Germain in July.
Inter Miami have not lost a game with Messi on the pitch and Martino said he would not have risked pushing the 36-year-old if it had not been for the cup final.
The Argentine coach said: "It's 90 or 120 minutes standing between you and the title. It makes sense. If it was any other kind of game, we wouldn't have taken any risks."