The report states Christie and Tierney still share a hotel room while on international duty and that Arsenal think that could put them in a good position to seal a deal if they were to make an official approach.
A substantial offer would be required to sign Christie, who has registered three goals and six assists in the Scottish Premiership this season.
Meanwhile, Arsenal announced on Thursday that left-back Sead Kolasinac will rejoin Schalke on loan this month.
Speaking at his press conference this week, Mikel Arteta insisted he wants to trim his squad.
“Well, we have a large squad, we knew that and a lot of things we wanted to do in the summer, we couldn’t accomplish for different reasons,” Arteta said.