As things stand, the Blues are on course to successfully defend the English top-flight title that they secured in record-breaking style last season.
Few are expecting the Reds to see the crown fall into their lap, but they can console themselves with a shot at European glory after booking a final date with domestic rivals Tottenham.
A sixth triumph will be chased down by the Reds, but Mills believes they would prefer to end a 29-year wait for domestic dominance while City are still longing for continental success.
"In an ideal world they would have swapped roles. City would have loved to be in a Champions League final," the former Blues defender told Sky Sports.
"Maybe not the fans but the club and where that takes them to a global level.
"Liverpool would quite happily be a point ahead going into the last game of the season and if they win they win the league.
"At the moment the league is probably a little more important to Liverpool because they haven't won it for such a long time.
"The Champions League, in terms of where City are, is a little bit more important but it hasn't worked out like that."
Ex-Liverpool full-back Stephen Warnock agrees that league success means more to the Reds at present, with it possible that missing out on the title could hit Jurgen Klopp’s side hard.
He said of a team that has suffered just one defeat this season and may end up on 97 points: "To have had both the seasons they have had, the form they have hit, records broken for both teams for games won.
"For Liverpool a record points tally in a Premier League season. It is just phenomenal. But that is the beauty of the league and that is why we love the game so much because the way it has gone.
"I think it would affect Liverpool more if they lost the league. How they would go on to next season. City are defending champions.
"We know how hard it is [to win back-to-back]. If it was to be Liverpool who lost out it would hurt them more."