Argentina's run to the final was thanks in large parts to Barca's Messi and Mascherano, while Alves played a part in Brazil's fourth-place finish at the World Cup, and new coach Luis Enrique now has the trio back available for selection in pre-season.
The back injury which ruled Neymar out of Brazil's World Cup semi-final defeat to Germany and the third-place play-off loss to Netherlands was evaluated by the Catalunya club's medical team and he will continue his recovery with a separate training regime.
"Neymar underwent a check up on his back injury with Barca this morning, with the club doctors expressing their satisfaction with his recovery which will continue with a specific training programme," a statement read. "His recovery will be monitored before a decision is made on a full return to training."
The returning players will train on Tuesday while the rest of La Liga's runners up in 2013-14 have been given the afternoon off.
Players who featured at the World Cup have been trickling back into Barca's squad for weeks since training recommenced under Luis Enrique on July 14, with those eliminated in the group stages being brought back first and the early knockout phase competitiors coming shortly afterwards.
Barca's pre-season schedule has been relatively low key so far, with just a 1-0 win over Recreativo Huelva and a 1-1 draw with Nice in three weeks of preparations for 2014-15.
However, they have three more friendlies scheduled - against Napoli, HJK and Leon - before they kick off their Liga season at home to Elche on Sunday August 24.
Following a season that ended with just the Supercopa to show for their efforts, Gerardo Martino's replacement Luis Enrique will be hoping to bring more notable successes back to Camp Nou this campaign.
Argentine duo return | Lionel Messi is joined by Javier Mascherano at training on Tuesday
Catching up | Gerard Pique and Lionel Messi in discussion at Barcelona's Sports Center in Sant Joan Despi