He said that King had "multiple offers," as a free agent and took his time before making the decision.
King entered the draft after being declared academically ineligible in July before his senior season.
He held a workout for pro teams last week at Georgia's practice fields, but was one of five players in the draft that were not picked.
"It's not disappointing when you get an opportunity to play at the highest level," said Conner who mentioned former Tennessee tailback Arian Foster and former Oregon tailback LaGarrette Blount as examples of players who had success recently after going undrafted.
Conner said King was looking for the best opportunity "to maximize his potential" and "to make an active roster." He was to leave for Minnesota Monday night.
The Vikings said they couldn't confirm until a player has signed. ESPN 1500 Twin Cities said King must pass a physical today before the deal is finalized.
The draft was conducted electronically from NFL headquarters in New York. Conner said he was with King when the seven rounds came and went without King getting taken.
King rushed for 1,271 yards and 10 touchdowns in three seasons at Georgia. He was suspended for two games last season and missed the Liberty Bowl after missing his fifth academic appointment. King started five games in 2009 and five in 2010.