Rodgers' exit came amid mounting pressure over results, including a shock Champions League qualifying defeat by Kazakhstan's Kairat Almaty and a 3-1 league loss at leaders Hearts which left Celtic trailing in the title race.
The club's former boss Martin O'Neill was appointed interim manager and the Northern Irishman has since guided them to a 4-0 league win over Falkirk and a 3-1 victory over rivals Rangers in the Scottish League Cup semi-finals.
Snoop Dogg, a hip-hop icon and long-time Celtic fan, said supporters would rather see Postecoglou at the helm, with the Australian manager available after being sacked by Nottingham Forest last month.
Postecoglou spent two seasons at Celtic between 2021-23, guiding them to two Scottish Premiership titles and a domestic treble in his second season before leaving for Tottenham Hotspur.
"I love sport, and in sport players leave, coaches leave, and you move on," Snoop Dogg told Scotland's Daily Record newspaper in an interview published on Sunday.
"You got to give Martin O'Neill big respect, he is coming back when we need him. I think you got to bring Ange back.
"The club are going to do what they are going to do, but the fans would love to see him back."
Snoop Dogg is well known for his love of sport and became an investor in Championship club Swansea City earlier this year.
The 54-year-old said he was keen on making a similar investment in Celtic, saying it was "something I have talked about in the past and if the opportunity was right I would be down for it.
"Celtic is a huge club and fans want to see the best players playing in this great stadium. All the owners have got to do is ask," he added.