The Brazil striker reacted angrily after the coach substituted him late in the game at the San Siro, which Zenit won 1-0.
Spalletti was seen extending his hand, trying to greet Hulk as he was leaving the pitch but the Brazilian just walked by without looking at the coach before having a heated discussion with the Zenit staff near the sideline.
"If the situation with the coach does not resolve itself I may leave the club in the January transfer window," Hulk, 26, was quoted as saying by local media.
Spalletti hit back at the striker after initially playing down the incident.
"Hulk can say anything he wants, but if I decide to change him during the game it means I'm not happy with his play," Spalletti was quoted as saying by local media on Wednesday.
"Hulk is mistaken if he thinks he should play for 90 minutes all the time. He said he wants to leave? Then, it's his choice and I can do nothing about it," added the Italian.
"As for myself, I'm not going anywhere."
Earlier Spalletti said: "All big players don't react well when they're substituted. The most important thing is that we won the game."
The Russian champions beat Milan thanks to a first half strike by captain Danny in their final Group C match to finish third and qualify for the Europa League.
Hulk has had a tough time settling in St Petersburg, with several senior Zenit players apparently unhappy after the club splashed out a Russian league record 60 million euros just before the transfer deadline to sign the striker.
Zenit demoted Russia skipper Igor Denisov to the reserve team in September after he refused to play, issuing an ultimatum to renegotiate his contract in line with what Hulk was making.
Denisov was later allowed to rejoin the first team after making an apology.