Coleman stated after Wales had reached the semi-finals of Euro 2016 that the current World Cup campaign would be his last in charge.
But Coleman's stance appears to have softened and he will speak to his Football Association of Wales employers about the future, probably before a planned Cardiff friendly next month.
Bookies have Giggs as favourite to be next Wales manager.
"There's a chance I can and a chance I won't," Coleman replied when asked if it was possible he could continue in a job he has held since January 2012.
"I can't give an answer right now. It's not just a matter of signing a new contract, the FAW have been great with me.
"I asked them to leave me alone as my contract has been running down and all the questions were getting asked.
"I wanted to concentrate on getting results. There'll be a conversation in due course and my contract is until the summer.
"But right now, I'm thinking about the experience. I'll go back to my family and take a bit of time.
"When the dust settles we'll see where we go."