After Kolkata, where Messi will play a short friendly match, he will head to Hyderabad, Mumbai and New Delhi.
In Hyderabad he will attend a concert in his honour and play another friendly.
He is reportedly scheduled to meet Modi in the capital.
Messi won his second consecutive Major League Soccer Most Valuable Player award this week after propelling Inter Miami to the MLS title and leading the league in goals.
The former Barcelona and Paris Saint-Germain attacker will spearhead Argentina's defence of the World Cup in June-July in North America.
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