Spurs beat Bolton 3-1 in their rescheduled quarter-final clash, while Everton won 2-0 at Sunderland in their replay.
The North London side will face West Londoners Chelsea – arguably their biggest rivals behind Arsenal – while Everton must play Liverpool.
"I am looking forward to a great weekend," Redknapp said. "They will be two great games, a London derby and a Merseyside derby. You wouldn't like to pick a winner. It is wide open."
Redknapp was also full of praise for Bolton keeper Adam Bogdan, who made several good stops before Ryan Nelsen broke the deadlock with 16 minutes left.
"Their keeper was amazing. I have never seen a keeper make so many saves," he said.
"He made save after save, we hit the woodwork. We had an incredible amount of chances. I always felt the goal would come."
Bolton counterpart Owen Coyle thanked the world of football, and Tottenham, for their support following midfielder Fabrice Muamba’s on-pitch cardiac arrest, which caused the match to be abandoned in the first half 10 days ago.
"It is the best game in the world and the events of the last 10 days have brought that home to everybody," Coyle said. "That strength of unity, that togetherness has been so positive and long may that continue.
"When we used to go to games and there was old-fashioned banter that was quite humorous, we have gone away from that. Sometimes people want to get abusive. But for the last 10 days at the games it has been incredible and I think that has been great. It shows football in such a good light."
Meanwhile, Everton manager Moyes insisted Liverpool will go into next month's FA Cup semi-final showdown between the derby rivals as favourites.
"Liverpool will be favourites. They have beaten us twice this year, haven't they? They have to go into the game as favourites, and we will go there and play.
"But the thing about Everton is they have got a history of being in finals, semi-finals, winning things. I have not been in as many as I would like to be, but I actually think there are mitigating circumstances for that in a way. But Everton as a football club are used to it, it's been there many times before and this isn't a strange place for them."
His opposite number Martin O'Neill admitted his side were simply not at the races as their hopes of making home advantage count proved forlorn.
He said: "Everton were better than us. They deserved to win the game. We didn't perform well enough - we didn't perform at all, and that's really disappointing.
"We were ready for the night and to see the sort of atmosphere just before kick-off, the noise level, was something we should experience more often here at the Stadium of Light. It was a great evening, a great night for football and we disappointed."