The team has a deadline of Tuesday (28 February) and the investigators had asked for an extension of a month from from acting president and prime minister Hwang Kyo-ahn.
The scandal has seen South Korea's parliament vote on 8 December 2016 to indict President Park Geun-hye, a decision that has to be upheld by the Constitutional Court.
The Yonhap news agency, citing sources, reported that the investigating team planned to indict Lee and former presidential aide Woo Byung-woo on Monday if it did not get the extension requested.
According to Yonhap, the Samsung Group is alleged to have signed a 22 billion won (US$18.3 million) contract with a Germany-based company owned by Choi Soon-il, a confidante of Park, and her daughter, under a consulting arrangement to pay for the daughter's equestrian training.
The investigators are examining whether this contract was signed as a quid pro quo for the state-run pension fund's backing of a major 2015 merger deal between Samsung subsidiaries.
Allegations have been made that the presidential office put pressure on the state fund to back the merger in return for the alleged favours that Samsung granted Choi.
Park, meanwhile, is waiting for the Constitutional Court to decide whether to uphold the impeachment vote which took place on 8 December 2016.
The scandal and its fallout comes after a year in which Samsung had to stop production of its flagship Galaxy Note7 after numerous devices combusted. The company also faced issues with washing machines and had to order a recall.
As a result of safety measures introduced after the Note7 fiasco, Samsung has not announced its new flagship, the Galaxy S8, at the Mobile World Congress which is underway in Barcelona this week. In the past such models have been unveiled at this event. The announcement is said to be delayed until 29 March.