Per Cadena COPE (via the Mirror's Natalie Evans and Jack Rathborn), Messi was provoked by an unnamed City player as the teams left the pitch and responded by insulting him.
The Cadena COPE report added (via Evans and Rathborn) that the 29-year-old superstar then had to be calmed by Argentinian national team-mate Sergio Aguero after he headed to the City dressing room for a confrontation.
However, Garcia reported that a City source denied there was any tunnel altercation involving Messi.
Meanwhile, Aguero played down the incident, per MailOnline's Sam Morshead:
Whenever you lose you're not very happy. I saw him there, he was feeling bad. I know him well enough to know when he's bad, when he's good. But when you lose, nobody's good.
I thought Messi said something to me but he didn't, and then we talked about other stuff. It was nothing serious. I heard something but I don't know what happened.
When someone loses you have to respect them. Leo wasn't in the mood to talk and I respect that.
Barcelona's defeat looked unlikely for most of the first half, as they completely dominated their hosts and went 1-0 up through Messi.
Indeed, according to City manager Pep Guardiola, his side played "the best team in the world" for the first 38 minutes, per Evans and Rathborn.
However, City got back on level terms in the 39th minute, when Sergi Roberto's mistake gifted Raheem Sterling the opportunity to set up Ilkay Gundogan for City's equaliser.
City was thrashed 4-0 in the reverse fixture at the Camp Nou last month, but they took the lead in Manchester on Tuesday when Kevin De Bruyne whipped a free-kick past Marc-Andre ter Stegen in the 51st minute.
Gundogan then wrapped up the points with his second in the 74th minute, earning City their first win over Barca in six attempts.
Per the Telegraph's Paul Hayward, it was a brilliant performance by City:
It was also Barcelona's first defeat of the 2016-17 Champions League season and not the best of nights for Luis Enrique's side.
They still top Group C with nine points, but Messi was seemingly not in the best of moods following the defeat.