The Super Eagles defender has proven himself in the heart of the Hibs defence with outstanding displays that fetched him one Championship player of the month award.
Hibernian lifted the Scottish Championship title on Sunday after ending the season with 71 points from 36 games and will play in the Premier division next season.
“When someone gives you the opportunity not once but twice, as he has with me, you want to give him a hug to say thank you,” Ambrose told Scottish Sun.
“He wants me to stay here, but we will see what the future holds. My agent will speak to the club and you never know what is going to happen.
“Of course, I’d consider staying with Hibs, because the fans showed me love and I enjoy working for the manager.
“I am out of contract at Celtic in June. I will go back for the rest of the season and from there you never know what is going to happen.”