The former Celtic captain has been without a club since leaving Aberdeen in March where he had been working as player assistant-manager prior to the sacking of Stephen Glass.
Brown parted company with the Dons after new manager Jim Goodwin relieved him of his additional duties, with the former Scotland midfielder opting to pursue other opportunities in coaching.
The 36-year-old is keen to take his first step into management, and has informed Raith of his interest in the role vacated by John McGlynn, who left the Kirkcaldy club this week in order to take over the reins at Falkirk, along with his assistant Paul Smith.
Raith finished fifth in this season's Championship, narrowly missing out on reaching the promotion play-offs for the second year running.
In his parting message, McGlynn insisted there is plenty of potential at Stark’s Park, stating: “We leave the club in a far better place than when we arrived, there is a good squad of players and with additions this summer, they can be a great team.”
Brown, who has also been linked with the Fleetwood Town vacancy, has been training with Dunfermline recently and was spotted in the Pars dug-out during the 0-0 draw with Queen’s Park in the Championship play-off semi-final first leg at Firhill on Wednesday night.
The Parkhead icon, who won 23 major honours across a 14-year career at Celtic, as well as earning 55 caps for Scotland, is one of a number of names under consideration by Raith along with his former Hibs team-mate Kevin Thomson.
The Kelty Hearts boss has emerged as a frontrunner having impressed in his debut season in the dug-out by guiding the Fifers to the League Two title by a 21-point margin in their first season in the SPFL.
The 37-year-old former Rangers star, who has also previously coached in the Ibrox youth academy, has already attracted interest from other clubs having been considered for the Kilmarnock job in January before losing out to Derek McInnes.
Ex-Raith players Danny Lennon and Laurie Ellis are also contenders for the Rovers hot seat, with Airdrie boss Ian Murray and recently sacked Dundee manager James McPake also linked. Applications for the position close on Friday, May 13.