City were found guilty of all charges relating to breaches of the league's financial rules over nine seasons from 2009-10 to 2017-18, as well as three out of four charges concerning failures to cooperate with the investigation.
The league said that City had used "sham" commercial contracts as part of schemes to inflate revenue and understate costs by more than £900 million ($1.19 billion) over nearly a decade, during which time they won multiple trophies. City have appealed the ruling and insist they are innocent.
Former Everton, Tottenham Hotspur and Barcelona forward Lineker said the whole debacle was damaging for the club and the English game, but that City admitting their guilt would go some way to draw a line under the saga.
"Obviously it looks really bad for Manchester City, it really does. And bad for the game... I'd love to see Man City now just own it and just say, 'OK, we got it wrong'," Lineker told reporters at the Leaders Week sports industry conference at Stamford Bridge.
"'But for the good of the game, we'll accept it, we'll accept whatever punishment comes our way and we'll carry on'. I think that would be a blessing and save their face a little bit at the moment, though that doesn't look very likely," he added.
"But it is damaging... and I feel for their fans, and I feel for their players."
Asked if City should be stripped of the three Premier League titles they won in the disputed period, Lineker said: "I wouldn't be surprised if it goes down that route. But again, ultimately, who suffers from that? The players and the fans."
The appeal will take place in private. It remains unclear whether sanctions will be announced before the appeal is heard, and whether they would take effect immediately.
City top the Premier League standings on 15 points from five games and seek a sixth straight win at Liverpool on Sunday.