The incident occurred in the tunnel at the Etihad stadium after full-time, with TV cameras showing the Romanian official asking Haaland to sign what appear to be one of his cards.
Former England international Owen Hargreaves blasted the act on BT Sport, saying: “You can be a fan, but you can’t do that in front of the other players, it just doesn’t look right.”
Ex-City defender Joleon Lescott added: “There’s never a right time for that, it just doesn’t bode well for the officials. It’s a childish thing to see.”
Haaland set up Marco Reus’ equaliser six minutes from time after Kevin de Bruyne had opened the scoring early on, but Phil Foden’s 90th-minute strike earned City a 2-1 advantage ahead of the second leg in Germany.
Dortmund had earlier been on wrong the end of a poor refereeing decision as Jude Bellingham’s goal was disallowed for a foul on City goalkeeper Ederson despite replays clearly showing the England youngster had beaten him to the ball.
City were also awarded a penalty midway through the first half, which VAR eventually overturned after it became clear that Emre Can had not felled Rodri.