What is Samsung's vice chairman being accused of?
Lee is facing bribery charges. It is alleged the company provided $36.42 million to businesses and foundations set up by a friend of Park to secure a merger between two Samsung affiliates.
The vice chairman, who was questioned for 22 hours over the charges last week, is due in court on Wednesday, where it will be decided if an arrest warrant is to be issued in his name.
The charges against Lee are part of a larger scandal involving Park.
Why is Park in hot water?
The controversy centres around Choi Soon-Sil, a close friend of Park.
Choi is accused of using her ties with the president to coerce top local firms, one of them Samsung, into "donating" nearly $70 million to dubious non-profit foundations which Choi then used as her "personal ATMs", in exchange for political favours.
Samsung is the single biggest contributor to the foundations set up by Choi, with a revenue equivalent to a fifth of South Korea's GDP.
How will this affect politics in South Korea?
Park has been impeached by the National Assembly but it is up to the Constitutional Court to uphold the impeachment. The hearings will go on until June.
If the court decides to go ahead with the impeachment, Park will be forced to leave office, and a presidential election would be held in 60 days from the decision. Former UN Secretary-General Ban Ki-moon is one of the likely presidential contenders. But he too faces an uphill task after his relatives were recently charged with bribery by US prosecutors.
What impact has this had on Samsung?
Samsung is already trying to rescue its brand after recalling some of its best-selling products.
Late last year, it recalled 2.5 million Note 7 smart phones after they caught fire due to faulty batteries.
There have also been reports of exploding washing machines.
News of Lee's possible arrest saw Samsung shares slide two percent on Monday.
Even though share prices steadied on Tuesday, Lee's arrest could have an "important" impact on the economy, a spokesman for the prosecutors acknowledged.