The ARU is in the process of replacing sacked Wallabies coach Eddie Jones, while the Reds are looking for a new coach for the 2007 Super 14 season, with current boss Jeff Miller stepping down after the competition's inaugural season.
There was some concern the two unions would be going head-to-head during their application process, however, Flowers said open communication will ensure this does not occur.
"We have had discussions with the QRU about our search and their search for a new coach," Flowers told the Sydney Morning Herald.
"It is a bit hard over the Christmas and New Year's break and we will be discussing it further this week when we return to work.
"But so far it has been along the line that there's no use them competing with us. We should be working on these things together."