Indications from Athens are the deal will go ahead in the coming week for a fee which will approach the £40 million the Seagulls paid Leeds for Georginio Rutter last summer.
Kostoulas, 18, is a versatile attacking player and has attracted considerable interest in a fledgling career which so far seen him made an impact in the Greek top flight and earn international honours up to under-21 level.
He is the son of former Greece defender Athanasios Kostoulas and his brother Konstantinos is also on the books at Olympiacos.
The outlay would be considerable by Albion standards and might hint at a major departure from the current squad.
Joao Pedro’s name is remaining prominent in broadcast and social media, with vague suggestions he will leave and intermittent mentions of Newcastle interest.
The message from Albion has been clear – they see him as a brilliant matchwinner still with lots of potential and look forward to seeing him reinvigorated in pre-season.
But that could also be interpreted as a reminder to potential suitors that he would command a big fee.
The Seagulls could also opt to realise assets who they did not use themselves last season and instead sent out on loan.
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Meanwhile, reports of Seagulls interest in a Marseille midfielder are being treated with caution and scepticism in France.
Foot Mercato reported Albion are pursuing Morocco international Azzedine Ounahi, who spent last season on loan at Panathinaikos, and had reached verbal agreement with the player.
An Argus contact in Marseille was less than convinced about that.
And the original piece itself stated there had been no negotiations between the two clubs.
