Celtic boss Neil Lennon admitted at the weekend that three clubs want his Nigerian stopper - Sunderland, Swansea and Liverpool
O'Neill is thought to be keeping tabs on the 24-year-old, even though Ambrose penned a three-year deal when he made a £1.5million switch from Israeli side Ashdod less than six months ago.
Ambrose netted in Celts’ 6-2 victory over Dundee United on Saturday.
But that came four days after he was blamed for two of Juventus’ goals in their 3-0 Champions League win over the Hoops.