The 26-year-old midfielder spoke at a press conference at France's pre-World Cup training camp on Sunday — the first time he had addressed the incident publicly since it was reported by Marca in early May.
"Obviously things happened — you could see and hear them in the media," Tchouaméni said.
"It got blown out of proportion because it came out in the press, and when you play for Real Madrid that creates a big reaction. A lot of nonsense was written. I read that there was a fight and that I had punched him — but that was not the case, although I won't go into details."
Valverde, who suffered a head wound requiring hospital treatment and stitches during the second of the reported incidents, had spoken earlier in the week upon arriving at Uruguay's training camp. He described the episode as a learning experience and said he had "the affection and support of Real Madrid and the fans" throughout.
Tchouaméni was direct about the relationship as it stands.
"With Fede, we have a common goal — winning titles with Real Madrid. There is no problem. If I face him at the World Cup, we will both want to win for our national teams. On a personal level, there are no problems with him right now."
He also addressed Kylian Mbappé's leadership within the France squad.
"He is a leader on the pitch and off it. He has the ability to connect with everyone. He is our captain and he leads by example."
On PSG's Champions League final victory over Arsenal, Tchouaméni was generous: "I think PSG deserved to win it. We are happy for them."
France open their World Cup campaign against Senegal on June 16. They are in a group alongside Senegal, the Netherlands and Uzbekistan — a group that does not feature Uruguay, making a Tchouaméni-Valverde reunion on the pitch contingent on both sides progressing deep into the knockout rounds.