While Renedi Masampu and Ludwig Francillette have not been retained following their Blues spells.
Gyollai has spent the last two weeks trialling at Fratton Park in an attempt to earn a deal.
Although contracted to the Posh for another 12 months, the Championship club have intimated they would be receptive to his departure by mutual agreement.
That would allow Pompey to sign the Hungarian youth international on a free transfer.
However, Cowley has still to make a decision on whether the 22-year-old has a Fratton future as he seeks competition for Alex Bass and Gavin Bazunu.
He told The News: ‘Dan has gone back to Peterborough for the time being, but no decision has been made.
‘We are looking at what we can and can’t do, what I can spend and what I can’t spend.’
Gyollai played 46 minutes in a Pompey XI’s 1-0 win over Bournemouth under-21s on Tuesday afternoon.
Joining him in the starting line-up for that Canford Arena fixture were Masampu and Francillette, who have since been released.
Former Chelsea apprentice Masampu was most recently with National League South side Dulwich Hamlet, while also had a trial at Sheffield Wednesday this summer.
However, the left-sided player didn’t do enough to warrant a permanent Blues stay following three pre-season appearances.
Former Newcastle United defender Francillette has also been trialling and was handed a start against Bournemouth under-21s.
The imposing centre-half was replaced by Academy youngster Izzy Kaba at half-time and has since left Pompey.
The former Leicester City winger was an unused substitute against Peterborough before handed 68 minutes on Tuesday.
A message from the Editor, Mark Waldron
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