Umtiti, 25, was linked with a move to the Emirates before the Gunners signed David Luiz and was also rumoured to be a potential makeweight in Barca's bid for Neymar.
"Honestly, I don't know where this rumour with Arsenal came from," he told Canal Football Club.
"Contacts with Arsenal? To be honest, I don't know if they had conversations with my agent, I just told him that I didn't care what was happening this summer and that it wasn't even necessary to talk to me about it.
"It was useless, I was going to have the same answer.
"My dream as a child is to play for Barcelona. Last season was the most difficult of my career, especially in terms of injuries."