The Villains showed a great deal of interest in the English prospect in January but Lutton rejected the offer.
The 21-year-old is also being chased by Premier league clubs Leicester City and Stoke City.
Having progressed through the youth ranks of the Hatters, Justin broke into the first-team in 2015.
The England U-20 international has been a regular for his side this season, bagging an impressive 11 goal tally, whilst primarily being a full-back.
He played a huge part for the Hatters to help them lift the League One title and was named the club’s young player of the season.
Why should the Lions move for Justin?
The Lions’ primary right-back options as of now tend to be Ahmed Elmohaamady and Allan Hutton and both of them are in the twilight of their career.
Mohammady has been brilliant for Deans Smith’s side this season but the chances aren’t great for him to continue on the long run given his age.
And Justin would be a great addition, whose versatility will bring a different dimension to Deans Smith’s side.
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Furthermore, the Lions are just a win away from playing in the Premier League next season and this could easily persuade the English youngster to opt a move to Celtic.
The Blue and Claret army will face Derby County in the Playoffs final on Monday.