Davis says the defender who could be joining Arsenal is Besiktas and Croatia international Domagoj Vida.
Vida has been linked with a move to the Emirates in recent days after leading his country to the World Cup final this summer.
And Davis explains injuries could force new Gunners boss Unai Emery into the market.
“If it is to be anybody, it’s likely to be a defender,” she told Sky Sports News.
“If you look at who they’ve got, Laurent Koscielny is out with his Achilles until December, Sead Kolasinac got injured in pre-season.
“Nacho Monreal is just on his way back but they are a little bit short there.
“Lots of speculation around the Croatian defender over the past few days, Domagoj Vida.
“He helped his country to the World Cup final, plays for Besiktas.
“The president has made it quite clear he was in London, he was Instagramming pictures of himself in London Park yesterday.
“And he has been quoted in saying ‘If it’s in the best interests of the club, we will let him go’.
“So that’s one that might happen a bit later.”