The 29-year old New Zealand international is currently training with the Dons and even though Brown is in desperate need of a new forward, he says Fallon would have to really impress to force the board to exceed their spending budget.
"He is a friend of Kari Arnason and we are giving him a training venue," Brown said.
"He is a nice, big chap who is visiting a friend and obviously he is out of contract and I am interested to see how he shapes up.
"We are not going to make a decision right now because I can't go to the board with another player and another player and another player.
"We have got to be sure if we are to go to the board as we are at our budget maximum already. I am reluctant to ask for dispensation unless we are absolutely sure."
Most recently he spent about four years with Plymouth Argyle before returning to Yeovil Town for a month's stay prior to the end of last season.