QPR owner Tony Fernandes would not confirm the signing but told Reuters at the British Formula One Grand Prix that the club would be making an announcement on Monday.
"Lots is happening in the club. We've signed five players, we've got a few more to announce," said the Malaysian aviation entrepreneur.
Reports said the agreement, which could potentially be worth five million pounds, will cost QPR an initial transfer fee of two million for the 31-year-old who, a year ago, signed a two-year deal to stay at United until the end of the 2012/13 season.
Park, who has made over 200 appearances for United since joining from PSV Eindhoven in 2005, has a reputation as a big game player able to relentlessly break up opposition attacks and send his own team-mates on the offensive.
He was the first Asian to compete in a Champions League final in 2009, and won four Premier League titles at United. The former captain of his country, he made 100 appearances for South Korea between 2000 and 2011.
South Korea is also an important growth area for Fernandes' AirAsia airline.
Park would be the second United player to move to QPR this week following young defender Fabio da Silva who has joined on a season-long loan deal.
Fabio, who can play at full-back or in midfield, has played 53 times for United, but has rarely been a first-choice starter.
He should get plenty of opportunities as QPR bid to establish themselves in the Premier League after staying up on the last day of the season following their promotion in 2011.
Fernandes said the club would probably sign three or four more players on top of those already announced before the start of the Premier League season.
"What [manager] Mark [Hughes] would like to do is have two people in each position," he said. "Now whether we get to that situation..."
QPR are also planning a new 40-45,000 seater stadium in West London and have hired architects Populous, who designed the new London Olympic Stadium and Silverstone's Wing pit and paddock complex.
That would be more than double the capacity of QPR's current Loftus Road home. Fernandes said those plans were looking good and a preferred site had been identified in the White City area.
"We could have sold 20,000 season tickets easily and I think with the investment in the squad and some of the ambitions that we have, and the catchment area that we are in, I don't envisage that it will be difficult to fill up," he added.
He said Populous would also be helping him with his new Caterham Formula One team headquarters at Leafield in central England as well as the development of QPR's new training ground in Ealing, west London.
"I'd like to try and make a Formula One, Caterham Cars, QPR kind of concept with maybe a hotel in the middle, kind of health and leisure," he added.
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