Milik has been wanting to leave Napoli since the start of the transfer window and the Sere A giants are also interested in selling him as he is in the final year of his contract.
Roma backed away from signing him due to the delays that the player faced in resolving outstanding financial issues with Napoli.
Juventus have also been keen on signing him, but it seems they are on the verge of securing a deal to sign Alvaro Morata.
Napoli are now pushing to send him to the Premier League and, according to Italian daily Corriere dello Sport, Newcastle could be back in the race for Milik.
The Magpies were linked with making an approach for the Poland international recently, but made no progress.
Newcastle are now considering tabling another offer and there is confidence that an agreement could be reached.
Tottenham have also been liked with an interest in Milik and a move to Spain is also believed to be another option for the 26-year-old.
