Byrne, 26, has failed to win a contract at Wigan Athletic and Paris Saint Germain following a series of trials during the summer.
He was released by Aberdeen at the end of the last campaign and did impress Dutch club NEC Nijmegen before travelling to Boundary Park for a trial.
"I had a couple of days with Oldham this week and I did well," revealed Byrne.
"(Manager) John Sheridan said he was pleased with me and I'll know next week if they have anything to offer me.
"I did okay in Holland but the deal there depends on them selling a player before I can come in, so I don't know what will happen there."