Roberts earned his seventh international cap for Wales in Friday’s defeat to Denmark. The full back is out of contract in the summer at his current club Swansea City.
The Express have reported that Rodgers is keen to add a right back to provide competition for Mikael Lustig.
Celtic can sign the 23 year old on a bosman this summer or for a cut-price deal in January.

Lustig has been a good servant for the club since signing from Rosenborg in 2011. The Swede made the right back spot his own for the last six years, making over 140 appearances.
He has been at the heart of Celtic’s success under three different managers. However, signs that he may be in decline are all too frequent.
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You only have to look back to RB Leipzig’s equaliser at Celtic Park. Lustig did not tuck in to help his centre halves, and the Hoops were punished.
It’s becoming increasingly more obvious by the week that Celtic will need to address this issue sooner rather than later.

The right man?
However, is Roberts the man to ease Celtic’s right back worries?
Roberts has made 21 appearances after graduating from Swansea’s youth academy.
He has enjoyed loan spells at Yeovil, Bristol Rovers and Middlesbrough, before cementing his place as Swansea’s right back this season.
With Celtic aiming to replace their established right back, is it a risk going for such an inexperienced talent?

There are good omens however for Roberts coming to Celtic.
His fellow Welshman Adam Matthews made the move from Cardiff in 2011, and enjoyed a successful four years at the club.
With Matthew’s career stagnating after leaving the Hoops, it could perhaps make Celtic an even more attractive option for Roberts.
It’s all talk at the moment, but Celtic do have to address their right back problem soon.
Could the Celtic fans have another hero named Roberts in the near future?