Jermain Defoe has hinted his future could lie away from Toronto FC after recent criticism from some of the club's fans.
Aston Villa have an option to sign Tom Cleverley from Manchester United in January.
The 22-year-old, a former France Under-21 international, was given the all clear to switch to the French club following an approach before the transfer deadline.
Gueye, who moved to Goodison Park from Strasbourg in June 2010, has made just six appearances for the Toffees this season.
Brest are currently only four points above the Ligue 1 relegation zone.