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 preseason.
The back injury which ruled Neymar out of Brazil's World Cup semifinal defeat to Germany and the third-place playoff loss to Netherlands was evaluated by the Catalunya club's medical team and he will continue his recovery with a separate training regime.
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"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 program," 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 the team has 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 competitors coming shortly afterwards.
Barca's preseason 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, the team has three more friendlies scheduled - against Napoli, HJK and Leon - before kicks off its Liga season at home to Elche on Sunday Aug. 24.
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