The club, owned by billionaire Sheikh Mansour's Abu Dhabi group, is one of nine that has been investigated and will receive sanctions for breaking FFP, along with Paris Saint-Germain.
These sanctions are believed to include a heavy fine and the reduction of their playing squad for next season's Champions League from 25 players to 21.
An announcement could be made on Monday as City's players enjoy a Premier League title-winning parade in an open top bus in Manchester.
Speaking on Sky Sports News, Swanson said: "It is hoped in the next few days, after a lengthy process, we will learn much more about Manchester City's fate and what the fine may mean.
"Sky sources told us last week that the club will be heavily fined - around £50m - and the squad for the Champions League will be reduced from 25 players to 21.
"We should find out early this week because of timing. UEFA have an executive committee meeting tomorrow and the Europa League final is on Wednesday.
"UEFA are keen to push this on and the big question for City that they must decide what they will do; accept the punishment or appeal it.
"But the big issue with an appeal is that it could lead to an even heavier punishment."
Both City and PSG were offered a settlement package by UEFA several weeks ago but negotiations have continued between the governing body and City in the hope of a lesser penalty.
UEFA and Manchester City have declined to comment.