The frontman played for his country in their 2-0 defeat to Chile in Santiago and appeared to be involved in an incident with opponent Gonzalo Jara.
Video footage shows a coming together between Suarez and the West Brom defender at a corner, after which Suarez appears to hit out in the direction of Jara's face.
Jara did not go to ground, with the pair instead trading words, while referee Nestor Pitana took no action, although he did later book Suarez for protesting, meaning he will be suspended for the next qualifier against Venezuela.
FIFA is still waiting on Pitana's official report, though, and will decide if any action is necessary after that.
In a statement on Wednesday, FIFA said: "We are still collecting all the post-match reports, since the officials have got 24 hours to send them. Based on the mentioned reports, FIFA will proceed accordingly."
The defeat has left Uruguay in sixth place in the group, outside of the top four automatic qualification places.