Brown is leaving Ashton Gate on a Bosman free transfer after deciding to try his luck at Championship level.
The 24-year-old is being courted by Preston North End and Queens Park Rangers, in addition to Stoke, and is due to make a decision on his future shortly.
But Potters boss Tony Pulis is optimistic of bringing Brown to The Britannia Stadium after working with the wide man earlier in his career.
"The discussions have been ongoing over the weekend," commented Pulis. "QPR and Preston are very, very keen but maybe the fact that I have worked with him and know him might push Aaron our way.
"I have told him to come to Stoke to test himself in the First Division and, fingers crossed, we will get him."
Meanwhile, The Robins have wrapped up their swoop for Orr on a free transfer after the midfielder had been released by Newcastle United.
The League One side set up the deal before the weekend and Orr signed a two-year contract after passing a medical on Monday.
