Newcastle United have long admired the England international, who is keen to leave the Etihad Stadium this summer in order to secure regular first-team football.
The Magpies held positive talks with Trafford's representatives last year while he was still at Burnley, only for Manchester City to activate a buy-back clause and re-sign him from under Newcastle's noses. With Gianluigi Donnarumma now first choice at the Etihad, Trafford has been reduced to a back-up role he is determined to move on from this summer.
Both Newcastle and Aston Villa are said to be keen on landing the 23-year-old, who will wait until after the World Cup before making a decision on his next move.
Villa can offer Champions League football, and speculation over the future of current number one Martinez has grown again in recent weeks, with reports in Italy suggesting Juventus are interested in the 33-year-old Argentinian. He also came close to joining Manchester United 12 months ago before ultimately remaining at Villa Park.
According to Birmingham Live, though, Villa will reject any offers for Martinez, suggesting he will remain Unai Emery's first-choice goalkeeper next season. That should strengthen Newcastle's position in the race for Trafford, though Chelsea could yet enter the picture as well.
Newcastle have already made several changes to their goalkeeping department this summer, having signed French youngster Ewen Jaouen while Odysseus Vlachodimos rejoins Sevilla on loan and Aaron Ramsdale returns to Southampton following his temporary spell at St James' Park.
John Ruddy and academy prospect Max Thompson have also left the club. There has also been interest in Nick Pope from Leeds United and Ipswich Town, though Newcastle will want a new first-choice goalkeeper in place before allowing him to depart.
Trafford, who is with Thomas Tuchel's England squad at the World Cup, has indicated he will review his future once the tournament ends.