The Lambs were in the hat for Monday night's third round draw after a shock win over Burton and will now face Tottenham at home.
Tamworth won 4-3 on penalties after a 1-1 draw against Burton and are the lowest-ranked side left in the FA Cup.
They are 16th in the National League table and behind fellow third round contestants Dagenham & Redbridge on goal difference.
With Premier League clubs now entering the fray in the FA Cup, non-league minnows Tamworth are set for a historic tie against Spurs.
However, manager Peaks revealed to talkSPORT beforehand that he's was hopeful of his side facing a team from the Championship.
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"I mean, from the club's point of view, obviously they'd like a big Premiership team I suppose, away from home to get a real good payday, one of the big clubs," he said on Baker and Jacobs.
"Me and my two sons are Leeds fans so I'd actually like to go to Leeds and sit in the dugout there I guess."
Championship clubs also enter the FA Cup in the third round instead of the first or second rounds of the historic tournament.
Leeds are currently third in the second-tier of English football and just three points off top, so would've certainly provided a strong test.
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National League sides such as Tamworth can generate huge and even season-changing sums of money with draws against top opposition such as Spurs.
Peaks explained the importance of this when he added: "I think the FA Cup brings a lot of revenue for non-league clubs.
"It's massive for us, especially as we're part-time in the National League, so obviously any extra income we can get is brilliant.
"You don't ever count on it because, as you two have just said, the beauty of the FA Cup is anyone can beat anyone on the day.
"So you can never budget for an FA Cup run but when you get one, and we've had a televised game, we've beaten a couple of League One teams, it's a massive bonus."
Tamworth first beat Macclesfield 4-2 in the FA Cup fourth qualifying round to reach the first round proper against Huddersfield Town.
They claimed a shock 1-0 win at home to the former Premier League side before knocking out their League One rivals Burton.
Goalkeeper Jas Singh saved two penalties in the shootout against the Brewers following a match that finished 0-0 after 90 minutes.
Both sides scored in extra-time and the scrapping of replays meant the match had to be decided there and then, although Peaks was eventually happy with the format.
"When it went to extra-time, it was level, we said it'd be nice to have a replay back at The Lamb [Ground]," he admitted. "But obviously once the penalties were done, we were quite happy with penalties!"
This season's FA Cup third round matches are set to take place from January 9 to 13.
Manchester United are the holders and have a huge clash against Premier League rivals Arsenal next month.