The 24-year-old centre-back - who recently featured for Nigeria at the Africa Cup of Nations in South Africa - has been in scintillating form in his debut season in the SPL, since arriving in Scotland from Israeli side Ashdod in the summer.
Liverpool boss Brendan Rodgers has been credited with an interest in bringing Ambrose to Anfield at the end of the season, though he is likely to face competition for the African's signature from domestic rivals Swansea and Sunderland.
Ambrose has scored three goals in 28 appearances for Celtic in 2012/13, and although he admits he's happy at Parkhead, playing for Neil Lennon's side, a possible switch to England would be of great interest to him.
"I am happy to be linked with a club like Liverpool," he admitted, in a post-match interview last week, after Celtic's 3-0 defeat to Juventus at Celtic Park in the first leg of their Champions League last-16 clash.
"My dream is to play across the border. The English league is the best but I am happy at Celtic. I love the fans here and we were unlucky against Juventus."
Liverpool are likely to be in the market for a new central defender, following the recent announcement that club legend Jamie Carragher will retire at the end of the campaign, to pursue a role in the media, as a pundit for Sky Sports.