That's because the 19-year-old was inspired by the Palace winger when both took up a place in the MK Dons squad.
Puncheon is a Spurs nemesis based on last season, of course, when he scored a late winner for Alan Pardew's men against the north London outfit. And he's a player Alli looked up to when he was younger.
Alli is quoted as saying by the Mirror: "He was a really good player and we always used to speak about how good he was.
"He was definitely a player I looked up to because he was really exciting to watch. When he was at MK he was a great player and everybody thought he was the best player there and he is showing how good he is now in the Premier League.
"It is going to be a bit weird playing against him, as I used to see him when I was younger, but I am looking forward to the challenge if I get picked."
It's no wonder Puncheon made an impact on Alli, with the 29-year-old lighting up the Premier League and shining with Crystal Palace, in particular.
Puncheon was simply too hot to handle for Tottenham back in January, although a poor display both in defence and midfield didn't help the north London side on that occasion.
Boss Mauricio Pochettino will be hoping for a much better return this time around and Puncheon's apprentice Alli could play a big part in that if he plays. The Spurs coach may want to give him a rest, though, after warning of the dangers of overusing him following the 3-1 Europa League win over Qarabag.