The showdown could happen if the Championship Addicks can see-off League 1's Sheffield United in their quarter-final clash, while Poyet senior's Sunderland must beat Hull City.
Poyet junior, who is now 18, remembers being at the old Wembley aged just five with his older brother Matias when the pair celebrated their dad's FA Cup win with Chelsea in 2000.
He would love to have more unforgettable Wembley memories against his dad in the semi-final, and, if the Addicks get through against the Blades, he hopes to avoid teams like Manchester City and Arsenal in the draw, should the Premier League duo progress.
Poyet junior told the Daily Mirror: "I've got pictures of me, my brother and my dad on the pitch at Wembley. From his days at Chelsea, that was the main memory. I was only five, I was scared and thinking: 'What's going on?'
"To be honest, I would love to play against my dad (in the semi-final). The way I see it, there are some very tough teams left in the cup, but if we did it then at least one Poyet will be guaranteed to be in the FA Cup final.
"The worst result would be getting Manchester City and if Sunderland got Arsenal, but if we play each other then we will go to Wembley again. It would feel really weird if we were both at Wembley for the semi-final.
"For me, it is massive. We are one win away from Wembley. I have only played six games, professionally. To be one win away from Wembley is amazing.
"It is a dream for a club like Charlton to be able to take 40,000 fans to Wembley. It would be absolutely amazing for us.
"I still take the FA Cup very seriously. I know my dad will never forget the day he won it. In the family, we will never forget how serious it is.
"I know, for Charlton, it is difficult to win the cup, but even to reach the semi-finals is unbelievable."