Barton, who joined Rangers on a Bosman this summer, has made some headlines in Glasgow despite not representing the Gers as of yet, and intimated that he was a much better player than the Celtic midfielder earlier this month.
The 33-year-old was given a bit of stick on Twitter after joining Rangers having previously suggested that he was a Celtic supporter, which Brown used as a stick to beat the former Burnley man with when asked for a response.
"I've not been in his league, he's in my league," he joked via BBC. "I think we'll get on really well, him being a Celtic fan, so I think we'll get on great."
The war of words between the pair is certainly whetting the appetite ahead of the return of Old Firm derbies next season, following Rangers' promotion from the Scottish Championship last season.
With both being midfielders, the duo might well see a bit of each other on the pitch come September 10 - the first top-flight meeting between the pair since 2012.
Rangers beat the Hoops on penalties in April as Mark Warburton's side reached the Scottish Cup final, which they lost to Hibernian.