The former Cork City and Sunderland forward has been granted permission to leave the League Two club in order to have a fitness test and discuss terms with the S.League side
As exclusively revealed by Goal, O'Donovan has been in talks with DPMM, where he could link up with former Cork City team mate Joe Gamble, and King says that he was willing to facilitate the former Republic of Ireland Under-21 international's wishes.
"If it favours the player, I'm all for that; if someone wants to do something then they can do it," King told the club's official website.
"I'll move on to the next situation. He's going out for five days to have a fitness test with a view to being offered a contract and he'll either take it or he won't.
"Once he said he wanted to take the opportunity, I said, 'fine, go, if it suits you I'll speak to the chairman and we'll see if it's something we want to take.'
"I believe it's the eighth of January when they will make a decision."
The 28-year-old has played in all four tiers of English football and was the League of Ireland's most expensive player following his move to Sunderland in 2007. O'Donovan signed for Northampton in January 2013 and he could now fill the fifth and final foreigner slot for DPMM, if talks are successful.