The midfielder's current deal expires at the end of the season and uncertainty surrounding his future began to grow after United postponed contract talks earlier this year.
Park's management agency JS Limited revealed to the Korean press that the protracted affair could be coming to an end, but admitted they are still in the early stages of negotiations.
"If the conditions are satisfactory, then the deal can be completed earlier. For now though, there is not much to say," the agency told Yonhap News in a statement.
"It is difficult to explain the specific details of the offer. But when an agreement is reached with United, an announcement will be made."
Earlier last month, United's chief executive David Gill stated that he expected Park to agree terms on a contract extension before the end of August.