Leonardo told the website of sports daily L'Equipe that "negotiations have stopped" amid reports that the player will Thursday reveal where he wants to end up when he returns from Argentina.
"We have stopped negotiating. We made a fine offer but we have been unable to reach agreement," said Leonardo. "Today there's not much movement in the (transfer) market. There was an opportunity and we studied it.
"We are not going to exaggerate when it comes to our proposals so we stopped - it's over."
The 27-year-old Tevez is also a target for both Milan clubs and is understood to prefer a move to Italy rather than France to end his exit at City.
He has been out of favour since he allegedly refused to take the field as a substitute in a Champions League game against Bayern Munich last September.
AC Milan are believed to be favourites ultimately to land the striker's signature but Inter harbour hopes they may yet win the race for a player that City say is worth 37 million euros.