Kostic is surplus to requirements at Juventus this summer and the club want to move him on before the window closes on Friday night.
West Ham wanted him last summer when he joined Juventus and the club have emerged as an option for him in the final days of the transfer window.
David Moyes has been keen to add a left-back and the club are considering signing him in the next day or so.
According to Italian outlet Calciomercato.it, the player would also prefer a move to the Premier League.
There are other clubs who have their eyes on him but Kostic’s preference is to play in the Premier League.
West Ham will sit down with intermediaries to see whether a deal could be agreed to take the Serbian to the London Stadium.
Juventus are open to a loan offer if the purchase clause is more or less guaranteed through certain conditions.
West Ham are keen but they need to sell a player before they can sign Kostic in the coming hours.
