Arsenal have made an improved offer in the region of £25m for Celtic left-back Kieran Tierney, Sky Sports News understands.
Sky Sports News understands that Serie A side Napoli are also interested in a deal for the Scotland international.
The 22-year-old was restricted to 21 league appearances for Celtic last term.
Tierney, who is contracted to Celtic until the summer of 2023, was hampered by a hernia problem last season and is currently recovering from surgery.
Celtic manager Neil Lennon said earlier this week: "He is still injured and he is rehabbing. He had a double hernia and he still has the osteitis pubis problem. Again, it is a slow burner that one."
Lennon also spoke of the need to further "trim" his squad earlier this week. Eight players have already left the club this window, including Mikael Lustig and Dedryck Boyata.
Along with the departures, the Bhoys have strengthened their squad, with the signings of Luca Connell, Boli Bolingoli and Christopher Jullien.
Sky Sports News reported this week Arsenal were set to secure a £27m deal with Saint-Etienne for defender William Saliba which would see the promising 18-year-old loaned straight back next season.
However that deal has been complicated after Tottenham also held talks with the Ligue 1 club, meaning it could be the player's choice if both offers are accepted.
Arsenal and Tottenham are also both interested in signing Real Madrid midfielder Dani Ceballos on loan, according to Sky sources.
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