The South Korean is a popular figure at Old Trafford but ambitious Bayern recognise United are approaching a transitional stage and want to tempt them to sell and help fund their rebuilding.
United manager Sir Alex Ferguson says he needs two players but privately there are concerns he will need at least four top level performers with question marks over Dimitar Berbatov, Michael Carrick, Rio Ferdinand and Nemanja Vidic, plus Owen Hargreaves still to prove his long term fitness.
Walk in Park: Ji-Sung has developed a useful habit of scoring in big games
Park, 29, has been a key figure in United's big games, scoring against Arsenal, Liverpool and AC Milan, but has endured fitness concerns himself following international matches involving long haul travel.
He is contracted until 2012 and only this week said he wanted to stay at Old Trafford for the rest of his career.
However, Bayern want to offer United a 90 per cent profit on the £4m they paid PSV Eindhoven for him in 2005 and that could trigger his departure.
United have their own targets in mind including Everton's Steven Pienaar, Valencia's David Silva and Sotiris Ninis of Panathinaikos but are still to determine their budget.
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