Manchester City and Leicester City have had bids rejected for Evans, with West Brom wanting a fee of around £30 million for the player.
City had been expected to make an improved offer, but Arsenal have now entered the battle to sign the Northern Ireland centre-half.
Arsene Wenger wants to strengthen his squad after his side’s poor start to the season and Evans’ experience could bring some stability to the Gunners’ shaky backline.
Evans is currently with the Northern Ireland squad ahead of this week’s trip to San Marino, but manager Michael O’Neil will allow him to leave their camp should he need to deal with transfer business.
The former Manchester United defender made almost 200 appearances for the Red Devils, before joining the Baggies in 2015.
He has established himself as a key member of West Brom’s defence and manager Tony Pulis has made no secret of the fact he would rather Evans remained with the club.
However, the prospect of joining one the Premier League’s big guns is likely to prove to tempting for Evans to ignore.