Mayor Stephanie Rawlings-Blake's administration has been immersed in talks for weeks with Dillon, who hopes to team with Baltimore investors to organize the race this year.
A Rawlings-Blake spokesman declined to comment on the negotiations. Dillon did not respond to a request for comment.
Councilman William H. Cole IV, a major supporter of the street race around the Inner Harbor that drew tens of thousands, said Dillon had not signed a contact with the city. The situation grows more urgent each day, because the new operator would need months to organize another race, he said.
"Time is not on our side," said Cole, who worked closely with the organizers of last year's race. "The hourglass of time is slipping away."
After city officials asked for proposals to take over the race early last month, only two groups responded: Dillon's team and an organization led by Geoff Whaling, who had worked on a Toronto race, sources said.
Officials focused on the proposal offered by Dillon, a familiar face to IndyCar racing executives and to city leaders, who say he won their trust during preparations for last year's race.
Dillon, who previously built tracks for IndyCar races in St. Petersburg, Fla. and Toronto, came to Baltimore weeks before the Labor Day event. Dillon served as general manager for Baltimore Racing Development, the organizer, in the month preceding the racing festival, and city officials credit him with pulling the event off despite leadership struggles among the company's top executives.
To organize this year's race, Dillon is reportedly teaming up with Felix Dawson, owner of investment firm Wilkes Lane Capital and an investor in Baltimore Racing Development.
Amy Konrath, a spokeswoman for the IndyCar racing league, declined to comment Thursday, saying the organization would remain silent "until the city has made an announcement." In the past, IndyCar officials have praised Dillon's work on races.
His company, Dillon Construction Co., is headquartered in Indianapolis, as is IndyCar.
Deputy Mayor Kaliope Parthemos, who is leading the city's negotiations, has said she hopes to present a contract to the city's spending board by mid-February. That would give a new team about six months to conclude sponsorship deals, market and sell tickets, and arrange logistics for the three-day festival.
Late last year, city officials yanked Baltimore Racing Development's five-year contract to organize the race, citing outstanding debts to city and state authorities, vendors and investors. According to internal documents compiled late last year, the company owes an estimated $12 million, including $1.5 million in city taxes and fees.
The race, which attracted more than 110,000 ticket-holders, was hailed as a success by IndyCar executives, who had been seeking a toehold in the Mid-Atlantic market.
Both IndyCar leaders, who have committed to 17 races in Baltimore and other locales in the coming season, and city officials, who invested more than $7 million in race preparations, have been pushing hard to continue the race.
Rawlings-Blake's administration has touted an estimated $47 million of economic impact that rippled through the region as a result of the race, according to a city-commissioned study.
Whaling, who submitted the second proposal to organize the event, said he had been largely ignored by the city. The chief executive officer of North American Motorsport Events Inc. submitted a 68-page-plan for the race earlier this week and said he has not yet received a response from the city.
Whaling's team proposes creating a nonprofit organization to run the race and would not assume any debt from last year's race. His proposal anticipates that the race would continue to lose money for the next two years, before turning a profit the following year.
"I haven't heard a word from the mayor's office" since submitting the proposal, said Whaling. "I'd like the courtesy of a response."