The 25-year-old winger played on loan for United from Forest from March until the end of the season.
The former Derry City star gave a good account of himself at the Seasiders, helping Southend get promoted from League Two to League One.
McLaughlin, who plays as a left-winger, scored twice in eight games with Southend during the two-month loan spell.
Brown has now said that he wants to sign McLaughlin on a permanent contract from Forest.
“Stephen is away at the moment too as Nottingham Forest are doing their pre-season training in Sweden but as soon as we’re both back it’s certainly something I will chase up,” the 56-year-old told The Echo.
Should Nottingham Forest sell Stephen McLaughlin?
McLaughlin has been on the books of Forest since 2013 and has a contract until June 2016, according to Transfermarkt.co.uk.
The 25-year-old has struggled throughout his time at the City Ground, and it makes sense for Forest to sell him.
Moving to League One is also going to help McLaughlin kickstart his career and rebuild his confidence.