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.
