Forman met with reporters on Thursday, a day after being promoted to his new position, and he said he believes Gordon wants to stay in Chicago.
"There's still a lot of steps until we get to that point," Forman added.
Gordon, who becomes a free agent on July 1, played a key role in the Bulls' impressive performance against the defending NBA champion Boston Celtics in the first round of the playoffs. The Celtics won the seven-game series that featured four overtime games.
Forman replaced John Paxson, who will remain with the Bulls as executive vice president of basketball operations. Forman is in charge of day-to-day basketball decisions, while Paxson will deal mostly with long-term organizational planning and talent evaluation.
Forman was on several college coaching staffs before joining the Bulls as a scout after the 1997-98 season.
"One thing I can tell you about Gar is that in the time we've worked together he's very organized, very detailed," Paxson said. "Growing up in basketball, he has coached and scouted and has very, very good eyes for talent and evaluation."
Paxson has been criticized for some of the decisions he made as general manager from 2003 to 2009. A trade he made last year, however, helped the team solidify around overall No. 1 draft pick Derrick Rose.
"Our goal is going to be to bring back the core of this roster, this playoff roster for next season," Forman said.
"I'm still going to be here, a big part of the organization -- I'm not going anywhere," he said.