The dismissal of Roberto Mancini following City's FA Cup final defeat to Wigan earlier this month has seen Brian Kidd take temporary charge of first-team duties, including Thursday night's 4-3 friendly win over Chelsea.
Malaga's departing Pellegrini is the red-hot favourite to take the post at the Etihad Stadium, but Richards says the new manager will have the full backing of the players no matter who gets the nod.
"That's in the papers (Pellegrini) so everyone's speaking about it. But you never know, there are sometimes late runners coming in. Whoever it is we'll be fully behind them," he told Sky Sports News.
Speaking of Malaga, Richards said: "They've been quality; they got to the quarter-finals of the Champions League. Obviously Roque Santa Cruz is out there and I sent him a text about three months ago and he said he's having a good time.
"It's all positive from Santa Cruz so hopefully, if he (Pellegrini) does come, he can bring it here as well.
"Managers are going to come and go. Mancini did a fantastic job in the three years he was here.
"The owners have decided they wanted a change.
"I'd like to thank Mancini for what he did. He brought an FA Cup, a Premier League and a Charity Shield," he added.
"For me, I'd never won anything before so I'm happy for that.
"But we're moving forward now; we're looking forward to whoever it's going to be and seeing their plans, the way they see the club and how far they can take us."