Southwest chief executive Gary Kelly is expected to attend the Wednesday morning meeting as well as Virgin America chief executive David Cush.
Both airlines would like to take control of two gates at Love Field that American Airlines is required to divest as part of its antitrust settlement with the U.S. Department of Justice. Currently, Delta Air Lines leases the gates from American and also wants to use the gates permanently.
Earlier this week, Virgin founder Sir Richard Branson held a party in Dallas to rally supporters for Virgin America.
Since Virgin America already has an agreement with American to take over the gates and is the Justice Department's only approved choice to receive the gates, Branson said he believes the fight should already be over.
"I think with Virgin competing against Southwest here, it will be good for the traveling public," Branson said in an interview on Tuesday morning. "If someone has 100 percent of the market, then fares will go up and the quality of service will suffer."
Follow @Sky_Talk or @andreaahles for live tweets from the city council meeting.
UPDATE 9:30 a.m.: Southwest CEO Gary Kelly is sitting here for the council meeting but I haven't seen Virgin America CEO David Cush yet. Quite a few media cameras here waiting for the upcoming agenda item on Love Field.