Manager Brendan Rodgers has said Liel Abada could leave on loan if the Israeli winger is “not at all suitable or ready” to play for Celtic.
The 22-year-old also missed last weekend's game against St Mirren and will also miss Saturday's game against Kilmarnock.
He is under pressure at home due to support for Palestinians among some Celtic fans.
Asked if a loan was an option, Rogers said: “It's a possibility, but we'll see. We'll work together.”
The Palestinian flag continues to be flown among Celtic supporters during the ongoing Israeli military offensive in Gaza.
Ultras group Green Brigade called on other Celtic fans to join in a song ahead of the game against Kilmarnock in support of the Palestinians.
“It's still the same situation,” Rogers said. “I've had a lot of conversations with Riel and I really empathize with his issues.
“This is more than football. It's on a human level and we have to respect that.
“He's training, he's on the road, but during this period it's all a matter of mentality and if you're not quite right or you're not ready, first of all, I'll let him know. I can't take any risks against them, because we always support the players and of course I have to protect the team.”
Approximately 1,200 people were killed in a Hamas attack on southern Israel on October 7 last year.
Since then, Israeli-launched attacks have killed more than 28,500 Palestinians and injured more than 68,000, according to the Hamas-run Health Ministry.
Rodgers had dinner with Abada to discuss the situation following Hamas' attack on Israel in October, but although the winger has recovered from injury and returned to the team, he has not been a regular starter.
“My job is not just to be a football manager,” said the Celtic manager.
“This is a young man, 22 years old, far from home. People can talk about what is happening there and then forget about it. This is the reality for him and this is It's his life. Every day.'' Every night, his family is at war.
“So it's a really, really tough situation for him. On a human level, I really, really empathize with him.
“It's sad. He re-signed with us because he had a strong belief that he could continue and develop. Then he was out for a while with an injury and now he's back and he's really convinced that he can continue to improve. , I feel like it's really a challenge. But I'm doing it here to support him and everything else is secondary.
“And when he's ready, if he's ready, he'll be able to give us everything.”