It had been suggested that the Dons would be among those keen to add Robson to their ranks after seeing him return to Britain from a disappointing year-long stint in the MLS with Vancouver Whitecaps.
Brown, though, claims to be well-stocked in midfield and in no need of the 34-year-old's services.
Instead, he intends to put any funds made available towards the acquisition of a new frontman.
Brown said in the Daily Record: "Barry is an exceptional player but I don't think I could justify signing another midfielder.
"We have plenty of provision there with Isaac Osbourne, Stephen Hughes and Rob Milson back from injury. Ryan Jack is also back from his broken leg next month.
"The budget is at its limit and the money for Ryan Fraser won't go to the team.
"But there could be a case to bring in another striker and that is something we are looking at."