The 25-year-old is out-of-contract at the Pirelli Stadium this summer, but the Brewers are desperate to hold on to him and have offered him fresh terms.
However, after they failed to win promotion in the League Two play-offs - Sky Sports understands that he looks set to leave with a host of clubs keen on him - one of which is Middlesbrough.
Boro boss Tony Mowbray made a personal check on Maghoma in the semi-final first leg against Bradford City - and is believed to have been impressed.
Boro's scouts have been tracking the skilful former Tottenham trainee for much of the season - where he has excelled with 17 goals from midfield.
A number of Championship clubs are believed to be keen on Maghoma, but Boro could be set to offer him the chance of a move to The Riverside.