Portugal face a daunting task against their bitter rivals and defending champions Spain in the semi-finals while England battle it out against Italy for a place in the last-four with Germany.
The Manchester United winger, who shares the dressing room with England players Wayne Rooney, Ashley Young and Phil Jones, said, "Maybe we can play England in the final."
"You never know what is going to happen. Anything is possible in football but first of all we have to win our next game in the semi-finals before we start to think about that," he said.
"The team is very happy because the performance against the Czechs was great. We scored just one goal but the contribution of the players is clearly getting better and better," Nani said.
Meanwhile, Portugal defender Miguel Lopes and winger Ricardo Quaresma clashed during a training session on Saturday. Lopes came hard on Quaresma, who reacted angrily to the challenge. The two were separated by coach Paulo Bento and defender Ricardo Costa, who later confirmed the incident to the media.
"There was rather strong challenge for the ball. We're virile, we always want to win challenges, and sometimes small incidents happen," The Valencia defender said during a press conference.