Nigeria international Ambrose has scored three goals in 28 games since arriving from Israeli club Ashdod last summer.
His performances are thought to have alerted a number of Premier League clubs including Liverpool, Sunderland and Swansea.
The 24-year-old says he is happy at Parkhead but admits it is flattering to be linked with an Anfield move and hopes to one day play in the English top-flight.
The centre-back, who suffered defeat with Celtic in the first leg of their UEFA Champions League last 16 tie with Juventus last week, said: "I am happy to be linked with a club like Liverpool.
"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."