The 76-year-old Lee, who was president from 2008 to 2013, reportedly denied all the charges against him and his wife during a 21-hour interrogation at the Seoul Central District Prosecutors' Office last week.
Prosecutors have said direct questioning of Kim is inevitable to ascertain Lee's criminal charges and indict him.
They are carefully examining the time and methods of grilling Kim in consideration of her status as a former first lady.
According to the sources, the most plausible option is to secretly summon Kim to the Seoul Central Prosecutors' Office in Seocho-dong, which is close to her home in southern Seoul. They said prosecutors' visit to her home or a meeting with her in another location cannot be ruled out.
The 70-year-old Kim, if summoned to the prosecution office, will be the nation's third former first lady to be questioned by prosecutors after the wives of former presidents Chun Doo-hwan and Roh Moo-hyun.
During questioning on March 14 and 15, Lee acknowledged receiving the National Intelligence Service funds, but he refused to explain how he spent the money. Prosecutors suspect Kim personally used the funds.
Prosecutors also suspect that Kim used the corporate credit card of an auto parts maker, DAS, to buy about 400 million won worth of goods from department stores and duty-free shops over a decade.
DAS stands at the center of the Lee scandal, as Lee is suspected of being its true owner. The former president has stubbornly insisted that DAS belongs to his older brother.
Prosecutors say Kim's use of the DAS credit card, if confirmed, could constitute an act of embezzlement because she had nothing to do with the company.