The Spain international scored an extra-time winner to secure a 2-1 win over Leicester City in the FA Cup quarter-final at the King Power Stadium last weekend.
Chelsea FC will face relegation candidates in the semi-final at Wembley with a place in the showpiece against Manchester United or Tottenham Hotspur up for grabs.
The west London side lost 2-1 to Arsenal in the FA Cup final last season despite winning the Premier League crown with two games to spare.
Pedro has enjoyed a decorated playing career so far after winning five La Liga titles, three Champions League crowns, three Copa del Rey cups and the Premier League at FC Barcelona and Chelsea FC.
And the Spanish forward underlined his desire to win the FA Cup in his third season at Stamford Bridge ahead of their semi-final clash on Sunday 22 April.
“Every game is difficult, for sure, and Southampton will be too,” Pedro told Chelsea FC’s website.
“We want to get to the final but first we have to beat Southampton and that won’t be an easy game, we will have to work very hard.
“For me, it’s very good if we can win this trophy. I haven’t done this in my career and it’s something I want to win with Chelsea, it’s a target for me and my team-mates. It’s a very good competition in England with a lot of history.”
Pedro has scored 28 times in 123 games in all competitions during two and a half seasons at the defending Premier League champions.
The Spanish forward netted 13 goals in 43 games during Chelsea FC’s title-winning season last term.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news