The Scottish giants could make a move for the Gunners defender in the January transfer window, according to The Daily Record transfer live blog on Thursday.
It has been reported that Bielik could leave the FA Cup holders for the Scottish champions on loan for the rest of the season this January.
Also, Polish champions Legia Warsaw have been reported to be interested in Bielik, who can operate as a central defender or used as a defensive midfielder.
Bielik is Polish Under-19 international and he has been on the books of Arsenal since the summer of 2015 when he joined the club for a transfer fee reported by BBC Sport to be worth £2.4 million.
The Polish is yet to break into the North London’s club first team fold and spent the second half of the last season on loan at Birmingham City in the Championship in England.
Rodgers’ side could do with another central defender, and the Arsenal defender could prove to be a smart short-loan signing.
In order news, Brighton and Hove Albion have agreed a deal to sign Hearts teenager Marc Leonard, who had earlier been reported to have interest from Newcastle United, Everton and Celtic.
Report from the Scottish Sun claimed that Hearts could bag a fee of about £350,000 for the 16-year-old, depending on appearances.
The Central midfielder has yet make a first team appearances for Hearts, who have handed the likes of Harry Cochrane, Jamie Brandon and Lewis Moore this season.