Evans has been attracting a lot of interest towards the end of the summer transfer window with Manchester City and Leicester City both reportedly seeing bids turned down by the Baggies.
FA Cup holders Arsenal, who have been linked with a move for the defender before, also threw their name into the hat for his signature as Arsene Wenger looks to strengthen at the back after a shaky start to the season.
A flurry of bids were expected to be lodged for the 29-year-old on deadline day but a move is looking increasingly unlikely after the West Brom captain was spotted with the Northern Ireland squad at Manchester Airport.
Michael O'Neill's men are due to fly out to San Marino on Thursday ahead of the 2018 World Cup qualifier and with the flight time taking 2 hours 24 mins, the period for a move to be completed is getting shorter.
The Baggies are believed to be willing to sell Evans although an offer of at least £30 million will be required.