Haaland may be Messi's main rival for the prize after scoring 52 goals in 53 games to help Manchester City win the treble of Champions League, Premier League and FA Cup last season.
Messi has 11 goals and eight assists for Inter Miami, which is eight points out of a playoff spot in the Eastern Conference with eight regular-season matches remaining.
The Argentine World Cup winner had limited involvement after entering with former Barcelona team-mate Sergio Busquets but made his mark on his regular season debut with an 89th minute goal.
Cincinnati led 2-0 on goals by Luciano Acosta in the 18th and Brandon Vazquez in the 53rd before Messi set up goals by Leonardo Campana in the 68th minute and seventh minute of stoppage time.
Messi had put Miami ahead in the 24th minute with a wonder strike into the top corner but Fafa Picault levelled for Nashville in the second half, taking the game to a shoot-out.
The winners will be announced at the Champions League draw on Aug. 31 in Monaco.
Messi will be playing the 42nd final of his career on Saturday, where Inter Miami will face Nashville SC in the Leagues Cup final.
Chelsea has agreed on a British record transfer fee of 115 million pounds ($146 million, 133 million euros) for Brighton and Hove Albion midfielder Moises Caicedo.
Miami will travel north to face the Philadelphia Union for Tuesday's semi-final after they beat Mexican team Queretaro 2-1.
Lionel Messi went to the top right of the goal with his freekick in the 85th minute, for a 4-4 tie, taking the match into a penalty shoot-out.
Messi scored seven minutes into the match and then added a second strike in the 72nd minute.
Inter Miami swept its group in the Leagues Cup and moved on to the round of 32 in the competition, in which it will host a to-be-determined opponent.
His magical left foot sent a free kick into the upper left corner of the net in the 94th minute giving Inter Miami a 2-1 win over Mexican club Cruz Azul.
"Leo's still going to need, no matter how good he is, no matter what his stature is, he and Sergio are going to need time to adapt no matter," said the Englishman.
The team will introduce him Sunday night at its stadium in Fort Lauderdale, and the first home match of the Messi era could be as early as Friday in a Leagues Cup match against Cruz Azul.
Messi reiterated earlier comments that he was unlikely to be in Argentina's squad when they defend their World Cup title in 2026.
The World Cup winner is expected to put pen to paper on a two and a half year deal, reported to be worth USD 60 million a year, before being presented to fans at a stadium event on Sunday.
The South Florida club also expect to complete the signing of another of Martino's former charges at Barcelona, Spanish midfielder Sergio Busquets.
Messi, 36, signed for PSG in the summer of 2021 after 17 seasons at Barcelona, but will now head Stateside to Inter Miami in the MLS after quitting the French capital.
After nearly two decades with Barcelona, Busquets announced last month that he would not return to the club. His contract expires at the end of June.