The Hoops were already looking to acquire a right-back after Mikael Lustig left the club earlier this month.
The Ladbrokes Premiership champions have now had to prepare for the possibility that Kieran Tierney will also need replaced, with Arsenal looking to sign the Scottish international.
A bid of £15 million has already been knocked back but the EPL are expected to return with a second offer.
Two players who could be brought in should Tierney go are Derby County’s Max Lowe and Rapid Vienna’s Boli Mbombo.
Lowe impressed during a loan spell at Aberdeen last season and has been on Celtic's radar over the past couple of months.
Copenhagen defender Peter Ankersen high up on the list of right-backs, along with Huddersfield Town's Tommy Smith.
Celtic are also keen to bring in another centre-back option with Filip Benkovic returning to Leicester City and Dedryck Boyata exiting the club last summer.
A bid of around £8 million for Toulouse defender Christopher Jullien is believed to have been accepted by the French club.
Smith's Hudderfield team-mate Mathias Jorgensen is another centre half Celtic are said to be looking at, along with Nantes rising star Nathan Gassama.