Sir Alex Ferguson revealed last month that a deal was on the table for the South Korean midfielder, who has been a key part of the United side since joining from PSV Eindhoven in 2005.
The player's father, Park Hyun-Jong, said: "I think both sides will be able to sign the new contract early this month, before the Premier League season kicks off.
"We first had discrepancies on the length of the contract terms, but it is now all settled.
"Actually, the two-year deal was initially proposed from our side."
Park, 30, has won four Premier League titles during his time at Old Trafford, as well as the Champions League in 2008.
Known for his tireless workrate and energy, he has scored 17 goals in 117 appearances and played in May's Champions League final defeat to Barcelona.
Source: Team Talk
Source: Team Talk