Both players will look to end a long hoodoo that has affected the two nations' superstars like Brazil's Pele and Diego Maradona of Argentina before them. Neither Messi nor Neymar has ever won the Copa.
That statistic will change for one of them in the dream final at Rio de Janeiro's iconic Maracana stadium.
For six-time Ballon d'Or winner Messi, this will be his fourth Copa final and perhaps his last chance to finish on the winning side.
He's been his team's standout performer, scoring four goals and creating five more – the tournament's leader in both categories.
But at 34, this may well be his last Copa and next year's World Cup could be his last major international tournament altogether.
So far, finals have led only to disappointment for Messi having lost in 2007, 2015, and 2016 at the Copa, and seen his side beaten 1-0 by Germany at the 2014 World Cup.
Some people believe winning something with Argentina is Messi's only remaining professional goal.
"We'll try to stop him from achieving this objective," said Brazil centre-back Marquinhos.
"As much as Messi, we also have players that deserve this title ... like our own 'Ney' who wasn't there for the last Copa," he added.
At 29, Neymar has a bit more time on his side but he was injured and absent two years ago when Brazil won their ninth title on home soil, beating Peru 3-1 in the final.
The two squads are impressive for their strength of depth.
In their semifinal victory over Peru – and despite Manchester City forward Gabriel Jesus being suspended – Brazil left the likes of Liverpool's Roberto Firmino, Flamengo hot-shot Gabriel Barbosa, and Real Madrid starlet Vinicius Junior on the bench.
In midfield, Liverpool's Fabinho has been kept out of the side by a resurgent Fred of Manchester United.
Neymar Jr's leg work and trickery could still rip defences apart when he is in his full flare and we can be sure he will be on his A-game on Saturday.
Likewise, Paris Saint-Germain winger Angel Di Maria – a bright spark when he came on in the semifinal against Colombia – has mostly started on the bench while new Barcelona signing Sergio Aguero has hardly had a look in for Argentina.
Messi and Inter Milan's Lautaro Martinez (three goals) have provided Argentina's main attacking thrust but they have quality and creativity throughout.
"Argentina are not just Lautaro and Messi, we cannot only concentrate on those two," said Brazil and Real Madrid midfielder Casemiro.
"They're great players, world-class players, but if Argentina have reached the final it's because of the (whole) group, we have to respect this."
As well as looking to end his career-long trophy drought with Argentina, Messi could make history in another way on Saturday.
He currently sits on 76 goals for Argentina, one shy of Pele's South American record of 77 national team goals.