Newcastle and Aston Villa have also had an interest in the 23 year old this summer, with the Magpies reportedly being deep in discussions over the past few weeks, talks that have not led anywhere between the two sides.
Trafford joined City last summer in a £27M deal from Burnley, a move which came only two years after City sold him for £14M.
Now, City look to offload the goalkeeper again in what is a bizarre piece of transfer business for the club who have failed to offer him first team football twice in his career so far.
Trafford was pushed out of the No.1 spot by Gianluigi Donnarumma on deadline day, leading to former manager Pep Guardiola leaving him on the bench.
He made just 17 appearances last season, with the vast majority of those coming in the EFL Cup.
Leeds are seeking a goalkeeper after Karl Darlow departed on a free transfer to Manchester United this summer and transfer expert David Ornstein has reported on Thursday afternoon that they are locked into talks with Trafford as Newcastle drop out of the race.
“Leeds United in talks with Manchester City to sign James Trafford. Newcastle United also interested & #NUFC made club-to-club contact, but 23yo #MCFC goalkeeper leaning towards Elland Road + #LUFC now working to land England international.
“Newcastle United no longer considering James Trafford as option for goalkeeper signing.”
Trafford initially joined City last summer with the full expectation of being their No.1 for the season and he departs once again disappointed.