Styles suffered relegation with Barnsley last season and faces a season in League One with the Tykes in the upcoming campaign.
However, the midfielder has only one year left on his contract with Barnsley and the club may want to cash in on him before his deal expires.
The Hungarian star could thus be out of the door this season and he has been linked with clubs in England this summer.
However, his destination could be Olympiacos this summer as they are interested in him, according to Greek daily Sportime.
The Greek side retained their league title last season and have Champions League football on offer, where they enter the second qualifying round.
While Barnsley were relegated last season, Styles impressed in midfield, making 43 appearances and scoring three goals.
Nottingham Forest were reportedly interested in him but have pulled out of the pursuit, while Fulham are also linked.
