FFA confirmed Lowy had been at Fifa headquarters in Zurich.
It's understood the A-League clubs, under the umbrella of the Australian Professional Football Clubs Association, have also made direct contact with Cook as the rift between FFA and the clubs turns acidic.
At the pointy end of the impasse is the make-up of the expanded congress demanded by Fifa and set to end the FFA board's effective control of the game.
The current 10-seat membership is made up of the nine state member federations, while the 10 A-League clubs collectively hold one vote.
Complicating the power struggle is the fight for money from the new TV deal, which is hindering the development of a new operating and ownership model for the competition.
Clubs are furious at FFA's refusal to grant what they believe is a fair share of A-League revenue, having rejected the most recent offer of A$3.55 million each per year, the most FFA says it can afford.
In the clubs' pursuit of at least A$4 million each, some owners are understood to be considering legal action against FFA.
They want to force the FFA to reveal details of its finance its finances, something the governing body believes it should not be required to do.