The South Americans face Nigeria in St Petersburg on Tuesday, knowing three points against the Super Eagles will send them through to the knockout stages, providing Croatia avoid defeat against Iceland.
Messi was among the players to train with the group but Gabriel Mercado, Nicolas Otamendi and midfielder Lucas Biglia all trained in the gym as they recover from minor knocks.
There has been speculation that coach Jorge Sampaoli would be sacked during the tournament with 1986 World Cup winner Jorge Burruchaga, the team’s technical director, set to replace him. However, the Argentina Football Association strongly denied this.
The midfielder sat out Friday’s session because of illness and again did not take to the field 24 hours later. The European champions face Iran on Saransk on Monday.
Moutinho has been a key player for his country after starting both of their games so far in Russia and provided the assist for Cristiano Ronaldo in their 1-0 win against Morocco.
There was good news though as left-back Raphael Guerreiro returned to training after missing Friday’s session due to pain on his leg.
Portugal, who are level on four points with Spain, require just a point against Iran to qualify for the knockout stage.
The Tottenham midfielder suffered a minor thigh injury against Tunisia and has been rated as “unlikely” to feature in Nizhny Novgorod by England boss Gareth Southgate.
While Alli took to the field alongside his team-mates on Saturday morning, he participated in the warm-up before carrying out individual drills away from the main group.
England were completing their final preparations at the Spartak Zelenogorsk stadium before flying to Nizhny Novgorod.
Alli helped England clinch a 2-1 victory in their World Cup opener on Monday, when he looked set to come off in the first half after suffering a knock.
A scan confirmed a quad injury that needed to be managed this week.
Southgate told talkSPORT on Friday: “We have to wait and see whether Dele is going to be fit. It’s looking unlikely because he has not trained with the team yet, but he’s progressing really well, so we won’t rule that out just yet.”