The 20-year-old joined the Citizens' academy at the age of 12 in 2015, but he is yet to make a senior appearance for the club.
Nevertheless, Trafford gained regular first-team experience during a successful 18-month loan spell with League One side Bolton Wanderers, who finished fifth in the third tier last season and won the EFL Trophy.
Trafford kept a total of 33 clean sheets in 74 appearances for Bolton across all competitions, including 22 shutouts in 47 League One matches last season.
The Carlisle-born shot-stopper has also starred for England at the European Under-21 Championships this month and is yet to concede a goal in four matches en route to the semi-finals.
Trafford's rapid rise at club and international level has caught the eye of a number of English clubs ahead of the new campaign including Leicester City and Leeds United, who were both relegated from the Premier League last season.
However, according to the Daily Mail, newly-promoted Burnley are on the verge of signing the highly-rated goalkeeper in a deal worth an initial £15m plus £4m in add-ons.
The report adds that a 20% sell-on clause could be included in the deal should the two clubs reach a formal agreement.
Burnley, who are managed by Man City legend Vincent Kompany, have already signed goalkeeper Lawrence Vigoroux on a permanent deal from Leyton Orient this summer.
The Clarets completed the signing of Arijanet Muric from Man City last summer and the Kosovo international established himself as the club's number one goalkeeper in 2022-23, featuring 41 times in their title-winning Championship campaign.
Bailey Peacock-Farrell is also on the books at Turf Moor, although he is believed to be facing an uncertain future at the club as he has just a year remaining on his contract.
Should Trafford complete his move to Burnley, the goalkeeper could make his Premier League debut at home against Man City in the opening match of the 2023-24 season on August 11.
Burnley have already strengthened their defence this summer with the arrival of Republic of Ireland international Dara O'Shea from West Bromwich Albion, while Jordan Beyer completed his permanent move from Borussia Monchengladbach in May following a successful loan spell last season.
The Clarets are also set to make Michael Obafemi's loan move from Swansea City permanent this summer, but it remains to be seen whether last season's top scorer Nathan Tella - on loan from Southampton - will remain at the club.