Leeds provided the shock of the third round when upsetting arch-rivals Manchester United at Old Trafford earlier this month and have the chance to create similar waves against Spurs.
Grayson said: "There has been a lot of media interest and that's what we want to do. This is what this club was all about a few years ago, in the Premier League and in Europe and we want to get the club back to the top.
"We know we need to get back into the Championship, that's the first step, we're having a good Cup run and we did well against Liverpool (in the Carling Cup) and Man Utd and it can only help the profile of the club and also the players."
Leeds have been held by Wycombe and have lost to Exeter and Carlisle since Jermaine Beckford's third-round winner at Old Trafford, prompting murmurings Grayson's players had succumbed to the fabled distractions of the Cup.
Most Leeds fans would happily forsake any cup run if it was to jeopardise their promotion charge, but the former Blackpool manager does not accept his players' performance levels have slipped.
He said: "Ultimately the league is the most important thing for us, but if you're winning matches it can't half give you a springboard and the confidence for the rest of the season, so we're really focused on what we need to try and achieve this weekend.
"If we don't win the game then hopefully we can take great heart in how we've played and look forward to the games after that.
"People asked about distraction in the previous round when we got drawn against Manchester United and the games between the draw and the actual match, I think we won four and drew one, so we were focused on what we needed to do in between.
"The players have also been focused between the Man Utd game and the Tottenham game. Results might have suggested otherwise, but I'm more than happy with how we have played. We've probably not had the breaks."
Grayson, confident of adding some new faces to his squad before the transfer window closes - "and a couple of decent players at that" - outfoxed Sir Alex Ferguson in the previous round and now takes on another managerial heavyweight in Harry Redknapp.
He added: "It's a big challenge. He's a fantastic character and I've a huge amount of respect for Harry. He's a great person to speak to. We were down at their training ground about a month ago and they made us feel very welcome down there.
"He's been there and done it. Through the lower leagues and up to West Ham and now Tottenham and Portsmouth previously. Harry's a character. Everybody you speak to in the game has got a huge amount of respect for him."
Tottenham v Leeds Correct Score: Leeds 1-0 20/1