"There is still a gap of some five million euros ($6.31 million) between us and Manchester United," Beckenbauer was quoted as saying by the SID sports news agency.

"Yet, (the) chances are pretty good."

Bayern's commercial manager Uli Hoeness said on Sunday that the club was in touch with United and had tabled a new offer for the 30-year-old who returned for pre-season training on Monday.

Nine-times European Champions Real Madrid are also targeting Van Nistelrooy, who was United's top scorer last season with 21 goals despite spending much of the latter part of the campaign on the bench after being left out by manager Alex Ferguson.

Bayern already have four strikers under contract in Claudio Pizarro, Roy Makaay, Roque Santa Cruz and Lukas Podolski.