It was suggested in France that Mane had agreed to join Real before Zinedine Zidane's resignation.
"I am very happy in Liverpool and my contract will last for three more years," the 26-year-old, a former Red Bull Salzburg player, told Salzburger Nachrichten.
"But you never know what will happen in the future. I want to win trophies, especially the Champions League."
Mane said it was tough to put the heartbreaking final defeat behind him but he has now turned his focus to Senegal's tournament in Russia.
"To be honest, this defeat was not easy to put away. The whole club worked hard for this Champions League title, but Real Madrid were the better team that day," he added.
"We lost to the best team in the world. The defeat is ticked off. Now it is time to play with Senegal (and have) a good and successful World Cup. That's my whole focus."