The Sharks had been considering shifting their home games to the ground when it is vacated by the footballers at the end of their season, but such a switch has been viewed as unviable by the club who will continue to play at Heywood Road.
Sharks Chief Executive Niels de Vos said: "The City Council has been very co-operative working with us, to discuss in detail the possibility of a move to Maine Road and we would like to thank everyone involved for their efforts.
"We have been very interested but unfortunately it is not possible to proceed to a successful conclusion which gives confidence that Sharks can operate viably at Maine Road. We are confident that both sides have done everything within their power to try to succeed but it is now time to move forward in another direction."
Maine Road Stadium will now be demolished when Manchester City move to their new home at the Commonwealth Stadium.
"We have explored fully a range of options with Sharks RUFC and we cannot find a situation which benefits both the city and the club," said Richard Leese, leader of Manchester City Council.
"We were very keen to see rugby at the stadium, but will now move forward and discuss with the residents a wide range of options to improve the area using different routes.Its been very helpful to explore all options with Sharks and we'd like to thank them for the time they have put into examining the possible development.We wish them well in the future."