The judge gave each side a week to present arguments for or against such an order in this case.
He can 'discuss foreign relations, immigration or Tom Brady as much as he wants to, ' she quipped, referencing the star New England Patriots quarterback before Super Bowl Sunday.
Jackson said it was her obligation to make sure he gets one and warned that Stone's public statements about the case could be used against him.
Stone has missed no opportunity to speak to the press since his arrest last Friday, appearing nearly daily on Alex Jones' Infowars show to discuss his case and booking an appearance on Tucker Carlson Friday night, following a whirlwind schedule of interviews with Reuters, CBS, NBC, and other outlets.
She said that if a gagging order was imposed, Mr Stone would still be able to talk to the media about issues not connected to the case.
Stone has hosted two press conferences and numerous interviews since his arrest one week ago stemming from special counsel Robert Mueller's Russian Federation investigation.
Indeed, Stone has been making the rounds in the media, giving press conferences and conducting interviews with national media outlets, including TV appearances.
This week, Stone pleaded not guilty to all charges, which included making false statements to Congress and obstruction of justice.
A gag order would not be entirely surprising; Jackson issued such a directive during Mueller's prosecution of former Trump campaign chairman Paul Manafort, which was a similarly high-profile case.
A status court hearing in the case is scheduled for March 14. Prosecutors said they had discussed possible October dates with Stone's defense, but Jackson said she was hoping for July.
"I testified truthfully on any matter of importance", he said.
The government said it also plans to turn over the contents of devices seized last week from Stone's home, apartment and office.
Trump denies collusion with Russian Federation.
Stone is free on a $250,000 personal recognisance bond on the condition that he not possess or apply for a passport and not travel outside southern Florida, the Washington area and New York City.
The indictment accused Stone of telling unidentified members of Trump's 2016 campaign team that he had advance knowledge of plans by the WikiLeaks website to release damaging emails about Trump's Democratic opponent, Hillary Clinton.
"I have great affection and remain a strong and loyal supporter of the president", Stone said.
Stone lied to Congress about those interactions and misled the congressional panel about his efforts to learn more about WikiLeaks' planned releases, the indictment said.
Stone said he did not even know for sure which Trump campaign officials were being referenced in the indictment and that he was never directed by the campaign to learn about future releases by WikiLeaks.