The Twins won the bid for Park with the Nexen Heroes for $12.85 million, but if the Twins and Park can't come to terms, Nexen will not receive the posting fee. The Twins, though, remain hopeful it won't come to that and an agreement will be reached.
The deadline for the club to sign Park is Dec. 8 at 4 p.m. CT.
Twins assistant general manager Rob Antony has previously said the club is confident it can come to terms with Park.
"We wouldn't have bid on him if we didn't believe or hope that we could get him signed," Antony said earlier this month.