The Daily Star Sunday says Park was signed from Monaco for £3million but is due to start a two-year military tour of duty in 2013.
The Gunners are currently investigating whether they can arrange for the South Korean captain to postpone his stint manning the border with neighbours North Korea.
A club spokesman said: "As it stands the player is expected to do his duty for his country.
"But as the captain of his international side, there may well be a case for extenuating circumstances.
"We are looking at the chances of postponing his service."