Blues completed the £6million capture of Serbian striker Zigic from Valencia on a four-year contract.
But his representative, Milan Calasan, revealed he had met with representatives of City in Switzerland en route to Birmingham.
And he claimed Villa had "begged" for the deal to be put on hold until Martin O'Neill returned from holiday.
He told the Birmingham Mail: "In Switzerland we met with a representative of Manchester City. We wanted to hear his plans before we met with Birmingham.
"They introduced into the game the eventual sale of (Emmanuel) Adebayor so it was immediately clear that everything was long term, so it was no surprise we automatically withdrew from everything.
"Then we were contacted by Aston Villa on the day Nikola had already arrived in Birmingham.
"They begged us to wait a while. Without Martin O'Neill, no decision can be taken and he is on holiday.
"In that case, there was nothing more logical than to finish a job with the club where all the doors were open (Birmingham).
"We had a great welcome from Birmingham. Alex McLeish (Birmingham) spent an hour chatting in the hotel to Nikola."
McLeish has now spent £12million on Manchester United keeper Ben Foster and Zigic so far this summer.
And he is set to step up his attempts to sign Wigan's Charles N'Zogbia after reportedly having an initial £8million bid rejected.