Two former Newcastle United players are already on the books at Brisbane Roar.
Ki was freed from his Newcastle contract in January, having made just four appearances all season.
And a move to Australian football has been mooted for the South Korean.
But asked whether Brisbane could be Ki's next destination, Fowler said, as quoted by The World Game: "I’m a realist.
"We can’t afford him and I don’t think anybody in the A-League could.
"I know he went to school here but we have to be realistic."
The Australian website reports that Ki earned an annual salary of A$3.5 million (around £1.8m) at Newcastle.
But the absence of a transfer fee could convince some clubs to take a punt on the 31-year-old.
Ki previously played for Celtic, Sunderland and Swansea City whilst in Europe, and appeared on around 300 occasions.
Fowler, the former Liverpool, Manchester City and England striker, was appointed as manager of Brisbane Roar late last year.
The 44-year-old spent two seasons as a player down under, representing North Queensland Fury and Perth Glory.
His squad contains two former Newcastle youngsters, Bradden Inman and Macauley Gillesphey.
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