The Brazilian was heavily linked with a move away from Old Trafford over the summer, with a number of clubs from the Saudi Pro League believed to be interested in his services.
However, the transfer window closed with the experienced midfielder remaining with Erik ten Hag's side.
The 32-year-old began the 2024-25 campaign in the first XI, but he has not started in the Premier League since the start of September, having dropped down the pecking order in terms of the midfield spots.
Casemiro has a contract with the 20-time English champions until June 2026, with the option of a further 12 months, but Brown has claimed that the club will attempt to offload him in January.
Man United 'looking to sell' Casemiro in January
"I'm told they'll look to cash in on him as soon as they can, on the 1st January if possible," he told Football Insider. "He's one of the biggest wage-earners and he's not going to feature regularly in the first team.
"He's been benched because he hasn't been performing and can't do it any more. I'm sure they would love to offload him if they could to get him out of the squad and off the wage bill, which would allow them to spend some money.
"Whether it's a move to Saudi Arabia or elsewhere, you've got to find someone who's willing to pay the money both to United and to him. They're not going to make back anywhere near what they paid for him but they'll look to bring in some money if they do let him go."
Casemiro was excellent during his first season at Man United, having arrived from Real Madrid in the summer of 2022, but he struggled to find his best form during the 2023-24 campaign.
Should Man United offload Casemiro in January?
Casemiro is Man United's highest earner on £350,000 a week, and he still has another two years left to run on his deal, having been handed a long-term contract upon his arrival from Real Madrid.
There is no getting away from the fact that the Brazilian has struggled over the last 12 months or so, though, and Man United should attempt to move him on in January.
A switch to another European club is highly unlikely, but there is thought to be huge interest from the Saudi Pro League, and a transfer to the division makes sense at this stage of his career.
A mid-season exit may open the door for the Red Devils to boost their squad in the winter window, with Chelsea's Ben Chilwell thought to be among the players on their radar.