No — there's no indication in the wiki that Jacoby Brissett is headed to the Browns. He's currently the Arizona Cardinals' QB1 (though in a messy contract standoff), and the only team floated as a potential trade destination so far is the Jets (from the Jacoby Brissett page).
The Browns already have a crowded QB room: Deshaun Watson and Shedeur Sanders are locked in a competition that head coach Todd Monken is letting "bleed into training camp," plus Dillon Gabriel and Taylen Green are also in the mix. Adding Brissett wouldn't make much sense for either side right now.