The Baggies have identified the Moroccan striker, formerly of Tottenham and Derby County, as an affordable recruit that could add quality to the Albion attack in the final third.
Fiorentina are willing to part with the 28-year-old Dutch-born forward after a poor season in Italy, but have come back with a counter-offer of their own which includes West Brom's highly-rated midfielder Mulumbu plus an amount of cash.
According to La Gazzetta dello Sport, West Brom have told Fiorentina that they will consider the proposal and will get back to them with an answer soon.
Mulumbu, 26, has one year left on his Hawthorns contract with a further one-year option after that, but the player has shown little intention of signing a new deal in recent weeks.
Mulumbu joined Albion from PSG for £175,000 in 2009 and Albion boss Clarke has been urging the club to extend his deal.