The Kaiserslautern midfielder has been personally watched by Neil Lennon as he tries to add to his squad for next season's campaign.
Ring, 23, only moved to the Bundesliga 2 side last season, but Celtic have stepped up their interest in the 23-times capped Finland internationalist, after Lennon also watched him playing in a World Cup qualifier against France this season.
"The matter has been under discussion for probably a year now," said his agent, Tuomas Talvitie. "However, we are a long way from reaching a conclusion."
His club are prepared to sell - despite only signing him a year ago - if Celtic make a good enough offer.