There is €3.5 million guaranteed to every participant of the pre-season tournament but one of the Italian clubs could find itself playing Europa League qualifiers instead.
Inter and AC Milan could be at risk of missing the International Champions Cup this summer due to a scheduling conflict with the preliminary rounds of the Europa League.
The third-qualifying-round matches in the Europa League are due to be played on July 28 and Aug. 4, with the ICC beginning on July 23 and concluding on Aug. 13.
Both Milan sides have signed up for this year's tournament, despite the risk that one of them could be forced to play in the early stages of the continental competition instead.