He will be the fourth goalkeeper at manager Pep Guardiola’s disposal, with Ederson, Stefan Ortega and Marcus Bettinelli already at the club.
It is anticipated Trafford will challenge Brazil’s Ederson, who has been first choice for eight years, for the number one spot.
Ederson is in the final year of his contract and has been linked with a move to Galatasaray, but last month described rumours of a departure “99% fake news”.
City have not received any bids for the 31-year-old, but there are doubts about the future of German Ortega given the increased competition for game time once Trafford arrives.
Trafford signed for City’s academy in 2015 but did not make a first-team appearance and spent time on loan at Accrington Stanley and Bolton Wanderers.
He has appeared for Burnley 73 times, including 28 in the Premier League in the 2023-24 season.
Trafford has represented England from Under-17 to Under-21 level, and was part of the winning European Championship squad of 2023, during which he kept six clean sheets and did not concede a goal.
He received his first senior international call-up in 2024 but has yet to make his debut at that level.
If he returns to the Etihad he will be City’s sixth signing of the window after midfielders Tijjani Reijnders (initial fee of £46.5m), Rayan Cherki (initial fee of £30.5m) and Sverre Nypan (£12.5m); left-back Rayan Ait-Nouri (£31m) and Bettinelli (nominal fee).
They also spent £200m in the January transfer window to boost their squad following significant injuries.