The Turkish sports newspaper claim that the clubs in mention have been keeping close tabs on the 20-year-old midfielder.
Newcastle and PSG are reported to be willing to pay €1.5 million for the young midfielder.
Serie A outfit Sampdoria are also reported to be interested in the Turkish youth international player.
Antalyali has represented the Turkish national team from U15 to U21 level and often wears the captains armband.
The young midfielder made a total of eight appearances in all competitions for Gençlerbirliği last season and attracted the interest of several of the Süper Lig giants.
The 20-year-old joined Gençlerbirliği on a £350,000 transfer from Buca last summer. The Buca academy has developed a reputation as producing some of the most sought after Turkish talents in recent years.
Salih Uçan was also from the same academy and was scouted by Manchester City and Villarreal before joining Fenerbahçe.
Uçan later joined Roma on a two-year loan with a future buy-out clause.