The 25-year-old impressed in his debut Boro campaign following his move from Nottingham Forest last July, scoring 15 goals in 47 appearances in all competitions.
Boro finished fifth in the Championship last season but faltered in the playoffs, losing 1-0 to Aston Villa on aggregate in the semi-finals.
As a result, manager Tony Pulis has planned a reshuffle of his playing squad for another season in the second tier and will listen to offers for Assombalonga.
According to the Birmingham Mail, the Baggies see the DR Congo international as a potential replacement for Salomon Rondon, who is thought to be edging closer towards a move to Newcastle United.
Assombalonga has also played for Peterborough United and Watford.