The 22-year-old was named in an initial 30-man squad for the Republic's training camp near Antalya this week ahead of Friday's friendly against Turkey, but was not among the final 25 who flew out from Dublin on Monday.
Manager O'Neill revealed that Kelly, who was born in England but represented Ireland at Under-18 and Under-21 levels, had declined the offer to join up.
"You might want to ask about Liam Kelly, who I think wants to keep his options open at this minute," O'Neill told Sky Sports News. "Obviously, he's born in England and wants to keep those options open and that's fine.
"I've always said here it's the player's choice, it's exactly what it is and if he wants to think that England might come in, that's entirely his decision.
"When we went into the squad, he had not returned a lot of calls coming through at the time. Despite the fact that I knew where he was born, I thought that was okay. I spoke to his agent some quite considerable time ago and I think that was always going to be okay, I felt."
Kelly was born in Basingstoke but qualifies for Ireland through grandparents from Mayo and Leitrim.