A total of 115 charges were issued against City earlier this year following a lengthy investigation into their finances between 2009 and 2018. The club have denied all wrongdoing.
Former Liverpool star Carragher told Monday Night Football: “Man City rightly so defend themselves and say they’re innocent of all charges. But if you’re innocent, why do people keep saying they’re kicking the can down the road, that it’ll go on for two to four years?
“Man City don’t want it, their supporters don’t want it. The Premier League doesn’t want it.
“It’s not good when we’re talking about one of the greatest Premier League teams we’ve seen of all-time, and [greatest] managers, that there’s this sort of asterisk above it until it’s sorted out.
“My message to Manchester City would be: this needs to get sorted. Sooner rather than later, just for your own reputation.
“Because there’s no doubt about it, if City are guilty then all this stuff we’re talking about will be tainted. In terms of Pep Guardiola, to get to the point of enticing him - the best in class manager they could get - they brought him to the club on the back of [what has led to] these charges.
“These need answering sooner rather than later and we can’t be waiting two to four years, because that is just a mess for Man City and also everybody else in the Premier League.”
Neville, formerly of Manchester United and England, insisted he has a “real problem” with FFP as a tool to protect the “established elite”.
However, he agreed that a ruling should be delivered soon for both City and the Premier League’s sake.
He said: “If the rules are in place, you have to abide by them. There is no doubt that for Man City’s owners and executives, if some of the most serious charges were brought forward and be proven guilty, the damage would be longstanding and they would be tainted.
“However, on the other side, if the Premier League were not to see through these charges the damage to their executive would be equally long lasting as well.
“There is a massive pressure moment coming in the next couple of years and it really won’t go away until its dealt with.
“I have to say, we need due process of course but this is a sporting situation not a criminal one - let’s move it forward and try and get it closed as quickly as possible.”