Lucas joined Liverpool back in 2007 from Gremio in a £5million deal and the midfielder has become an integral part of the first-team squad, making 241 Premier League appearances since arriving at Anfield.
However, the Brazil international, whose last cap came in 2013, has struggled for playing time this season under manager Jurgen Klopp and he's only made 12 league starts.
The 30-year-old's contract with the Reds expires at the end of the season and the club will reportedly not be offering a new deal, spelling the end of a 10-year stay.
Several teams are said to be showing an interest in the soon-to-be free agent but it is Celtic, who stormed to the league title again this term, that are believed to be leading the race.
Bhoys manager Brendan Rodgers worked with Lucas when in charge at Liverpool and the duo could be reunited as the Scottish outfit look to build a squad capable of going far in the Champions League next term.