The 24-year-old Mali international enjoyed an impressive Ligue 1 campaign last season, playing a key role in Lens’ push for Champions League qualification and their historic Coupe de France triumph.
According to L’Equipe, an agreement between the two clubs is now close for a €48 million deal - roughly £41m.
Lens have been in discreet negotiations with Brentford for several weeks as the Premier League club prepare for Jordan Henderson’s expected departure to Chelsea.
However, Brentford could face competition from Crystal Palace, managed by former Lens boss Pierre Sage.
The Eagles are reportedly considering making a stronger offer for Sangare as they look to beat their London rivals to the midfielder’s signature.