Nagelsmann, now in charge of RB Leipzig, grew up a Bayern Munich fan and was hoping to see his side clinch a treble against United in the 1999 Champions League final.
Bayern were up 1-0 heading into stoppage time before Teddy Sheringham equalised and Solskjaer netted a dramatic winner in one of the most famous nights in United's storied history.
The result saw Man Utd clinch a treble of their own, and Nagelsmann has said he still hasn't completely recovered from that heartbreaking defeat.
"The first thing is, I'll tackle him down tomorrow," Nagelsmann joked about the current Man Utd head coach.
"I wasn't the happiest person. My dad was a Gladbach fan at the time, and he annoyed me a bit. He was happy that Bayern didn't win. I wasn't that happy."
"I will still greet Ole Gunnar Solskjaer in a normal way of course and no longer be angry.
"Ryan Giggs, Rio Ferdinand, Paul Scholes, Ruud van Nistelrooy, Ole Gunnar Solskjaer – there have been a few very, very great players who have been there and are currently there still.
"It's a club with a lot of tradition."
United got off to a slow start this season, which reached a low point in a 6-1 hammering at the hands of Tottenham before the international break.
Solskjaer's side have shown improvement after the international break though, defeating Newcastle and PSG while drawing with Chelsea at the weekend.
Nagelsmann is wary of his opponents on Wednesday, noting their improved recent form.
"The last few games have gone in the right direction. They are difficult to defend and have a lot of quality in the final third," he said.
Still, Nagelsmann is confident his side have enough to win the game and maintain a perfect start in the Champions League after last week's 2-0 win over Istanbul Basaksehir.
"We are confident enough to say that we want to win the game," Nagelsmann said. "Six points at the start would be excellent and a step on the way to the next round."