The South Korea international is reported to be keen to join the Latics, having become frustrated with his lack of first-team opportunities at the Emirates Stadium.
However, according to The Mirror, Wigan are struggling to come up with a financial package that suits the Gunners.
The 28-year-old, who spent last season on loan at Celta Vigo, is believed to earn around £50,000 per week.
Park has made just six first-team appearances for the Gunners since signing from Monaco two years ago.
His current contract is due to expire in June 2015.