Four-time Premiership winner with Celtic open to return
The Nigerian is a free agent after leaving Derby County in the summer.
Ambrose, a four-time Scottish Premiership winner with Celtic, left Hibs in January to join Frank Lampard's Rams but he failed to make an appearance for the Championship outfit.
A fan favourite at Easter Road, the 30-year-old has played more than 250 games in Scotland.
He told the Daily Record: “I would never say never about the possibility of coming back to Scottish football.
“It is a great place to play football and I feel the Scottish league is growing and getting better.
"The standing and reputation of the league is growing and there is a real profile to it with the likes of Neil Lennon and Steven Gerrard now at Celtic and Rangers.
“I have had some great times in Scotland. My times there, with Celtic and Hibs, were amongst the best of my career and if there was interest there then it is something I would definitely consider.”
Ambrose, who has been signed by Celtic boss Neil Lennon twice, revealed he had turned down a big-money offer from a Turkish side.
He is currently training with Narayi Celtic Kaduna in his native Nigeria waiting for his next move.
“I have been training every day with my local team back in Nigeria and playing in friendly games.
“So when I get my next move sorted, I will be ready to hit the ground running and to be able to get up to speed very quickly. That was the problem when I went to Derby last season.”