The ban on trading players in to the club was introduced in September.
It came after negotiations with the AFL that led to the club being given two years to phase out its cost of living allowance (COLA).
The delegation attending AFL House on Monday included senior coach John Longmire, football department head Tom Harley, CEO Andrew Ireland and president Andrew Pridham.
A Swans spokesperson told AFL.com.au the club was pleased to be able to state its case to the AFL Commission and would now await its decision.
The club had no further comment to make at this stage.
Having been banned from the 2014 trading and exchange period, the Swans are hoping to be allowed to recruit free agents and trade in players at the end of next season.
The club is understood to be frustrated with the AFL's decision given it did not break any rules in its use of COLA, but has made no public comment about the ban since it became public midway through the trade period.
AFL CEO Gillon McLachlan conceded to AFL.com.au on the day of the NAB AFL Draft in November there was a possibility the ban could be softened and admitted that the decision could have been communicated better after it was made.
The Swans shocked the football world when they snared key forward Lance Franklin at the end of 2013, signing the ex-Hawthorn star to a nine-year contract.
That coup caused an outcry, and the AFL came under further pressure from Victorian-based clubs, which complained about the Swans' access to NSW-ACT Academy players when their recognised the talent emerging from that program.
The Swans got academy graduate Isaac Heeney with pick No.18 in the NAB AFL Draft and expect to draft Academy graduate Callum Mills next year.
It is likely to have to pay more in real terms for Mills than Heeney as the AFL attempts to introduce a revised bidding system.
This year the Sydney Swans traded out Shane Biggs for a draft pick to the Western Bulldogs.
Hawthorn is the only one of the 10 clubs since 2005 that has won a premiership after letting two drafts pass without trading in a player.
However the Hawks used the draft to bring in experience during the 2006-2008 period by recruiting former Port Adelaide premiership player Stuart Dew.
