Sinclair has been searching for a club after being released by Leicester City at the end of last season after a turbulent campaign on and off the pitch.
The 32-year-old could not help to keep The Foxes in The Premiership and was also embroiled in a sexual assault case following the club's mid-season trip to La Manga.
Although he was acquitted of all charges, he is now aiming to revitalise his career and will spend a few days training with The Bees in an attempt to hone his fitness.
Bees boss Allen confirmed Sinclair is with the League One side but acknowledged there is healthy interest in the versatile stopper.
"I can confirm that Frank Sinclair will be training with us for a few days which will help him get fit for the new season," Allen told the club's official website.
"Several clubs are interested in Frank and if moves to these clubs fall through I would have an interest in Mr Sinclair."
