Brazil superstar Neymar was one of five players sent off amid an ugly fracas at the end of Sunday's Classique, which Marseille won 1-0 at the Parc des Princes.
A VAR check showed Neymar striking Alvaro on the back of the head and he later posted on Twitter to say his only regret was not hitting his opponent in the face after alleging he was subjected to a racial slur.
Alvaro denied the claims with his own post on social media and Tuchel was asked about the incident at a post-match news conference.
"What I heard? He [Neymar] told me that it was some racist insult, but I did not hear anything on the pitch," Tuchel said.
When made aware of Neymar's social media post, Tuchel replied: "I think that everyone has the same opinion that racism in all the society, in sports or in our lives can't exist. It's obvious.
"But I did not hear that today, neither [did] the referee so I can't answer this question."
Marseille boss Andre Villas-Boas earlier said he too was unaware of the incident, while also speaking about Alvaro's claim he was spat at by PSG's Angel Di Maria.
"I don't know. I hope not, there is no place for racism in football," Villas-Boas said in an interview with Telefoot.
"It's a serious fault if it happened but I don't think so. Before that, we had a situation with a spit from Di Maria.
"These are things to avoid in the world of football. I hope it won't be a black spot in this historic performance."
PSG have started their Ligue 1 campaign with back-to-back 1-0 defeats, with their domestic season have been delayed due to their run to the Champions League final.