Watt, who famously scored in Celtic's 2-1 Champions League victory over Barcelona in 2012, flew out on Monday morning ahead of the proposed move.
Watt spent last season on loan at Belgian side Lierse, scoring eight goals in 17 games, but he fell out with manager Stanley Menzo in March and was demoted to their 'B' squad. He did not play for the club again, returning to Celtic at the end of the season.
The 20-year-old was involved in Celtic's pre-season training camp under new manager Ronny Deila but did not feature in either of the club's Champions League qualifiers against Reykjavik.
Liege are believed to have met Celtic's valuation of the player, and will hope to complete a deal in time to register him for Wednesday's Champions League qualifier against Panathinaikos.
Watt made his debut for Scotland Under-21s in August 2012 in a friendly match against Belgium. He went on to make a total of nine appearances for the U21 side, scoring five times.