first time this week when his girlfriend, Antonella Roccuzzo, gives birth.
The couple's baby, already known to be a boy who will be named Thiago, was widely expected to arrive at the weekend. That prompted feverish speculation in the Spanish media that Messi would be rested from the team.
"The game against Deportivo (on Saturday) could go down in Messi's history books. Several sources report that the Argentine has the date of 20th October marked on his calendar as the day his first child, Thiago, will enter into the world," claimed Marca sports daily.
"Messi himself has confirmed that his family and that of Antonella are on their way to Barcelona for the occasion."
In the end, baby Thiago decided not to make an appearance just yet and Messi played in the 5-4 win over Deportivo La Coruna, scoring his 21st Barcelona hat-trick which kept his team on top of La Liga.
With or without Messi, Barcelona are in pole position in their European group after back-to-back victories.
They can take a significant step towards qualifying for the last 16 if they come out on top against Celtic. The Scottish club managed a surprise win away to Spartak Moscow in their last game to leave them second on four points.
Despite regular centre-halves Carles Puyol and Gerard Pique having spent most of the season in the treatment room, Barca have been a model of efficiency.
Although they haven't reached the peak of recent campaigns in terms of performance, only the El Clasico draw against Real Madrid has stopped them from boasting a perfect winning Liga record.
Messi once again showed his importance to the team with a hat-trick at the weekend and he now already has 15 goals this season. His tally for the calendar year is up to a remarkable 71.
Barca dismissed any fears of tiredness as they stormed into a three-goal lead away to Deportivo, but a harsh penalty awarded for a foul by Javier Mascherano allowed the Galician side back into the game.
In the end they were left holding on for the final 10 minutes with just a goal advantage and down to 10 men following the dismissal of Mascherano.
Xavi Hernandez and Pedro Rodriguez started the game on the bench, given a break ahead of the visit from Celtic, but coach Tito Vilanova didn't risk dropping Messi who had been on international duty with Argentina.
With Puyol and Pique still not fully fit, it's likely that Mascherano and Alex Song will be the centre-half pairing against Celtic.
Puyol remains sidelined with a dislocated elbow, while Pique is still struggling with an injured left foot sustained against Spartak in mid-September.
"He has stayed at the gym to do specific work," said a statement from the club.
With Dani Alves at right back also injured, youth product Martin Montoya should keep his starting position. In midfield, Sergio Busquets will be missing through suspension.
Celtic warmed up for the clash with a 5-0 victory over St Mirren and manager Neil Lennon then flew to watch Barca in action against Deportivo.
"It will be awesome if we can get something out of the match but it won't be great if we lose the game," he said.
"I'm taking a pragmatic approach and we are not going to get carried away by the surroundings, that is for the supporters. The players have to go there and compete and do themselves justice."
Lennon feels the team has grown as the season has gone on.
"We weren't great at the start. We had the (Champions League) qualifiers which was our short-term aim but now we are in there the players are believing that they are good enough to play at that level."