Following Friday's news conference ahead of the club's Premier League game against West Brom on Sunday, Times reporter Tony Barrett confirmed the news:
Liverpool's interest in England international Richards was reported by Sami Mokbel of the Daily Mail Online, who wrote, "Manchester City have rejected a cheeky loan bid from Liverpool for defender Micah Richards."
The Reds are on the lookout for new defensive recruits after suffering from a number of injuries. They are particularly short at right-back, where first-choice Glen Johnson is currently crocked.
As reported by BBC Sport, when Johnson's injury was confirmed, Rodgers said the player would be out for an indefinite period:
"The timeline he'll be out will be indefinite really. I just think it's now at that point where we need to get him right."
Meanwhile, Richards has struggled for regular football at City this season due to the exceptional form of Pablo Zabaleta and a hamstring injury. Per ESPN FC, he has managed just two Premier League starts.
However, with the club chasing silverware on four fronts, manager Manuel Pellegrini would be foolish to allow Richards out on loan and leave himself short.
The move makes perfect sense for both Liverpool and Richards, though. The defender would get the first-team football that could help him force his way back into the England setup ahead of the World Cup this summer, while the Reds are in desperate need of a defensive boost.
Richards, who can also play at centre-back, would be able to slot into Liverpool's side without any problems. His athleticism and ability to support attacks would likely be of particular interest to Rodgers.
With the deal unlikely to happen, Rodgers must now hope his side's lack of defensive cover doesn't catch up with them and hinder their chances of Champions League qualification.