The Scottish champions are being linked with a move for Kieran Tierney, who played for them several years ago.
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Tierney is a free agent in the summer, as his Arsenal contract is expiring and he will not be offered a renewal.
On the possibility of signing Tierney, Rodgers stated: “Well, Kieran’s someone I know really well, but there’ll be lots of players that are linked with coming to Celtic, so we will never speak about a player, especially a young player that is at another club.
“But, we’ve got work to do; we know that, we want to improve the squad further and a number of key areas.
“Until that happens, the players here have been working so well and we’ll just continue to work with them and see what happens in January.”