Mr Ban's term as the world's top diplomat expires at the end of December.
In his final press conference as UN chief, Mr Ban said that after some rest he will return to South Korea and consider how best to help his country.
South Korea's next presidential election is scheduled to be held in December 2017.
However, a poll could take place within two months after the country's parliament voted to impeach current President Park Geun-hye over an influence-peddling scandal.
Ms Park is accused of allowing a close friend to profit from her connections with the presidency.
If the country's constitutional court upholds last week's impeachment vote, she will become the first sitting South Korean president to be deposed in the country's democratic era - and a new presidential election will be held within 60 days.
The constitutional court has 180 days to make a final ruling.
Mr Ban's comments come amid ongoing protests in the South Korean capital, Seoul.
Large crowds are expected to gather this weekend to demand that Ms Park resigns immediately, and to urge the constitutional court to formally remove her from office.
This will be the eighth consecutive week of protests against Ms Park.
While the rallies have been largely peaceful, there are fears that demonstrators could clash with thousands of the president's supporters who have planned their own protest near the court.
Ms Park's lawyer, Lee Joong-hwan, has said the court should restore the president's powers because there is insufficient evidence to justify her removal.
The case against Ms Park rests on her relationship with long-time friend Choi Soon-sil, who faces charges of coercion and abuse of power.
It is alleged that after Ms Park became president in 2013, Ms Choi, 60, used their friendship to pressure powerful corporations into donating to foundations she controlled and then siphoned off funds for her personal use.
Prosecutors say Ms Park had a "considerable" role in the alleged corruption. The president has denied that, but apologised for putting her trust in her jailed friend.
Ms Choi's criminal trial will begin on 20 December.
UN Secretary General Ban Ki-moon has hinted that he may shortly run for the presidency of his native South Korea.