Beckham's new team will make their debut in the MLS in 2020, and the former England captain is understood to want to bring in one of the world's top players as a marquee signing.
A host of high-profile players have been linked with the club, but the Daily Mail reports that MLS executives are confident Beckham will look to prise Messi away from Barcelona.
The five-team Ballon d'Or winner is contracted to Barca until the end of the 2020-21 campaign, but will be 33 when Inter Miami come into existence.
Beckham is reportedly hopeful that both Barcelona and Messi might be tempted by a mega-money bid at that stage of the attacker's career, despite the Argentine's previous insistence that he wants to finish his career at the Camp Nou.
Messi has spent his entire career to date with Barcelona, scoring 556 goals in 642 appearances for the club.