The former Spurs midfielder helped set up a meeting with his old club after United beat Birmingham 2-1 in a third round replay on Tuesday night.
Veteran Brown, 35, said: “It’s fantastic for me against my old club but it will also be a great tie for Leeds, especially at Elland Road.
“I love the FA Cup. It seems to be falling away a bit with some fans. But the players were talking before the Birmingham game and we all said it is special – it certainly is to me anyway. I hope it will be a great game with Spurs at Elland Road.
‘‘The atmosphere there when we played Chelsea in the Capital One Cup was fantastic and that’s want we want to re-create.We’ll certainly have to be on our game and on our guard all the time.
‘‘Once you give top sides a goal or a chance you get punished, as we found out when Chelsea beat us. So we will be as solid as we can.”