The report also suggests both the Scottish giants have been scouting the centre-back for a while.
Moreover, the Hoops are said to be edging out their arch-rivals for the transfer as Neil Lennon looks to reinforce his defence.
Lennon has held talks with the recruitment head Lee Congerton for the signing of Czech defender who is valued around £5m. (h/t The Sun)
The Czech Republic defender spent his youth career at his country club Sigma Olomouc before joining Chelsea in 2010.
Kalas was subsequently loaned to Vitesse, FC Koln, Middlesbrough and Fulham since joining the Stamford Bridge.
His longest spell was with the Lilywhites where he went on to make 76 appearances.
Kalas made his international debut back in 2012 and has earned 18 caps thus far.
The 25-year-old can also play as a right-back at times.
How Kalas could be a good signing for Celtic
Despite having extended his contract in 2017 for another four years with his parent club, the centre-back is well aware of his bleak future.
The Hoops are currently running out of defenders as Boyata is expected to move as a free agent and the on-loan players Filip Benkovic and Jeremy Toljan are set to return to their parent clubs.
Lennon was appointed as the new caretaker manager after Brendan Rodgers left Celtic Park to become the new manager of Leicester City.
Ever since then, the former Celtic Captain has led his side to two victories and a draw in three matches.
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The Hoops are slated to face the winners of the Light Blues and Aberdeen clash in the Scottish Cup semi-finals.