Following a breakdown in attack during the Blaugrana's 2-0 victory over Granada, Messi lost his temper and appeared angry at his fellow forward for not providing a better pass in the box.
Villa responded to the reigning Ballon d'Or winner unkindly and the two then argued on the pitch for a few seconds, leading to reports that the pair are not getting along at the Catalan club.
However, Thiago has played down speculation that there is any serious disagreement, and has instead explained that emotional arguments are just a normal part of the game.
“It is normal in football for that to happen, it was just a discussion,” the 21-year-old told reporters after the match.
“It shows the ambition of the players to keep growing. Everyone wants to improve and it is very normal. We’re playing football and sometimes we are under pressure."
The Brazilian-born Spaniard also cited the volume levels at Camp Nou as part of why the players looked so riled when talking to each other.
“There are 90,000 people in Camp Nou and you’re playing football, you have to shout.”
Barcelona are presently in first place in La Liga, one win away from matching their best start in team history if they can make it six wins out of six against Sevilla on Saturday, September 29.