A DESPERATE scramble is under way as Hong Kong's myriad of pop promoters fight among themselves to bring this year's hottest act - the Eagles - to town. But the way things are shaping up, getting the band to sign on the dotted line will be the easy part. Finding a financially viable venue will be another matter. Reunited after 15 years, and currently filling US stadiums to the rafters, the Eagles will be playing in Japan in early December, after which a window of opportunity exists for another Asian date. We understand that Singapore, Taiwan and Thailand are also keen to host the concerts. But the band members themselves would prefer to come to Hong Kong, which is understandable since it will bring them here with just a few shopping days left before Christmas. The band has stipulated that they must be back in the States for the Christmas holiday. Since the last Tokyo gig is on December 15, and allowing a day to travel from Japan, that conceivably leaves the days between December 17-21 for the Hong Kong concerts to be staged, before the Eagles must take flight to return home. This, however, is where things get - to use the title of an Eagles hit - desperado. The Hong Kong Coliseum, which is the only suitable venue, is booked from December 15 until the end of the month for a series of Faye Wong Ching-man concerts, with most dates being sold out already. As one exasperated promoter told us: ''It will all be up to Faye Wong's manager whether the Eagles play here or not.'' Meanwhile, every promoter one talks to seems to be bringing the Eagles to Hong Kong. But as a spokesman for the band's management, the William Morris Agency, said yesterday from Los Angeles: ''It's still all up in the air.''