Celtic have had a bid of around £1.5 million for the midfielder rejected by the Easter Road club.
Ambrose, a Nigerian international, spent five years at Celtic, claiming six major honours, enjoying victory over Barcelona and reaching the last 16 of the Champions League. He said: “I think John can make the step up. He has the quality and the ability to succeed at Celtic. If he does get there then he will need to battle for his place because it’s not easy at a club like Celtic.
“There are quality players all around you and they will all want to play. Celtic is a place that comes with huge responsibility and the fans are special. If he does join them, then that is just football and we would wish him well.”
McGinn, who has also been linked with English Championship clubs, has 12 months to run on his current deal, and has been valued at £5m by Hibs boss Neil Lennon.
Ambrose, the 29-year-old defender, added: “I am not surprised to see Celtic come in for a player of John’s quality. The most important thing is he has done so well for this club and has helped put us in the position we are in today.
“It’s a big compliment to Hibs that Celtic are looking here for players. When you are doing well people look at you and this squad did well last season.”