The 24-year-old is currently with Genk, who are hopeful of keeping their prize asset, but Boro have made a late bid to try and lure him to England.
Celtic had been linked with a move but a deal failed to materialise and now Boro are hoping that a late swoop could be in the offing.
Sky Sports understand that Boro have tabled a bid close to £4million for Vossen as they look to bolster their strike-force ahead of a push for Premier League promotion.
Despite Boro not being in the top flight it is understood that Vossen would be willing to make the move if a deal could be struck between the two clubs.
The North East outfit failed with a £2million bid for Leeds striker Ross McCormack late last month and Tony Mowbray is desperate to get a top striker in before the window closes.
Former Norwich striker Kei Kamara is also in talks with Middlesbrough ahead of a move from Sporting Kansas, and his move should be confirmed before Monday's deadline.
Meanwhile, it is understood the Riverside club have fended off interest in captain Rhys Williams on deadline day, with Wigan among those keen on the Australia international.