West Ham are in the market for a striker after they sold Sebastien Haller to Ajax earlier this month for a fee of €25m.
They made a concrete move for Sevilla striker Youssef En-Nesyri and tabled a bid worth €30m for him, but the Spanish club knocked back the offer.
West Ham have called off their pursuit of the Moroccan for now, despite signs that Sevilla would be willing to deal for around €40m.
The Hammers are considering other options in the market and it has been claimed that Maja is one of the players the club are tracking.
The London-born forward spent four years at Sunderland before he left the club for French outfit Bordeaux in 2019.
The 22-year-old has scored eleven times for the French club in the last 18 months and would represent a much cheaper option for the Hammers.
He is one of the players West Ham are weighing up making a move for in the final two weeks of the winter window.
Maja worked under Moyes at Sunderland and could reunite with his former manager at West Ham again.