City met Scunthorpe on Wednesday night in the Round of 16 in this season's competition, in which van Veen got on the scoresheet twice and set up an assist as the League Two side saw off the young City side.
City deny the allegations but said that words were exchanged between the pair after van Veen pushed Harwood-Ellis into the hoardings during the contest.
After the match, the Dutch striker tweeted: "If u need down to earth players and players who don't cash anyone off and giving it the big one give me a ring Man City with all due respect.
"#2goalsandassist. On to the next round we go."
Van Veen also told BBC Radio Humberside: "He cashed me up really, saying, 'I've got more money than you.'
"If you play at City it's great, one of the biggest clubs in the world, but I just told him if I can score twice against you, what do you think Harry Kane is going to do to you?
"He did not take that well and basically cashed me up. I just looked at him and thought, 'Why are you giving me the big one, you have not really done anything yet.'
"If I was in his position I'd never be cocky or arrogant. I'm not saying all of them were but the centre back was. I'm happy I scored two and basically shut him up."