The Celtic boss faced questions over a transfer swoop for the left-back as he spoke to Sky Sports on Friday morning.
Tierney has been heavily linked with a return to Glasgow after news broke that the clause for an extra year in London will not be triggered by Arsenal.
🗣️ "We have work to do. We want to improve the squad further."
Brendan Rodgers on Celtic's January transfer window plans and a potential return for Kieran Tierney ⤵️ pic.twitter.com/xqXYXq7HO9
— Sky Sports Scotland (@ScotlandSky) December 20, 2024
But, Rodgers has remained coy over a move for Tierney but admitted "we've got work to do" ahead of the transfer window next month.
"Well, Kieran is someone I know really well but there's lots of players who have been linked with coming to Celtic.
"We will never speak about a player, especially a young player that's at another club.
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"But we've got work to do, we know that. We want to improve the squad further in a number of key areas. But until that happens, the players here have been working so well.
"We'll just continue to work with them and see what happens in January."
More to follow.