Banza scored 21 times in the Portuguese top flight for Braga last season and is expected to move on in the coming months.
West Ham are interested in signing him and have already sent an offer to the forward for a summer switch.
However, their proposal is reportedly not anywhere close to the offer he has received from clubs in Saudi Arabia.
And according to Italian outlet Tutto Mercato, West Ham will face further competition as Roma are now considering making a move for the Braga forward as well.
The Serie A giants are in the market for a striker and are assessing several targets ahead of the summer.
Banza’s performances have been noticed and his name is on their shortlist of targets for Roma.