The 28-year-old, who earns around £70k-per-week at the London club, has struggled with fitness and consistency this season, managing only 21 appearances.
However, there is no doubt about his talent and potential, and when fit he can be a real asset for any side. He is versatile and can play in multiple positions.
Antonio is currently out injured but Palace are keeping a track on his fitness, and have made him their top priority signing in the summer transfer window.
The report claims that the Eagles have not only made his signing a priority but they could look to firm up their interest with an offer.
Antonio joined the Hammers from Nottingham Forest in 2015, and has scored 20 goals in 76 Premier League appearances.
His main strength is versatility and has played as a winger, forward and even in defence as a right-back for the Hammers. He would be a cracking signing for the Eagles, but they expect West Ham to ask a high transfer fee for him.