Park has become available from Monaco after their relegation.
Gavin Law, the group head of corporate affairs for Liverpool sponsors Standard Chartered, said earlier this season: "We would love the club to have players of nationalities from the markets in which we operate. Look what Park [Ji-sung] has done for [Manchester] United in terms of coverage in Korea.
"Liverpool are more aware than most other clubs we've spoken to of the commercial opportunity for them. If they can sell a million shirts with another Mr Park on the back, why wouldn't you?"