The Magpies have already spent an initial £18.5m on highly-rated Frenchman Ewen Jaouen this summer, but Howe wants a more experienced addition who can come straight in as his No.1, with Jaouen viewed as the long-term understudy while he adapts to Premier League football.
Nick Pope remains Newcastle United's current first-choice, starting Saturday's pre-season friendly against Darlington before being replaced by Jaouen at half-time as the entire team was changed.
Pope is expected to be allowed to leave if Newcastle land a replacement, with Leeds United and Ipswich Town both credited with interest, though no firm offers have yet been made and Newcastle would not sanction a sale until his successor is in place.
Trafford, 23, remains second choice at City behind Gianluigi Donnarumma, who arrived from Paris Saint-Germain at the end of last summer's transfer window, despite the England international winning both the FA Cup and Carabao Cup last season.
Trafford has made clear he wants to become England's undisputed No.1, telling reporters: "History says yeah. There hasn't been a goalie start for any of the top nations that isn't a No.1 at the club."
His position in the pecking order was underlined again on Saturday when Dean Henderson, rather than Trafford, was selected ahead of him for England's World Cup bronze medal match against France, with Thomas Tuchel instead opting to rest Jordan Pickford.
With Pickford's own position now under scrutiny after a mixed World Cup and a home European Championship on the horizon, both Henderson and Trafford have an opportunity to stake a claim to be England's first-choice goalkeeper, though Henderson's current status as Crystal Palace's regular starter gives him the edge for now.
That dynamic adds further urgency to Trafford's decision over his club future this summer, with Aston Villa, who can offer Champions League football, also showing strong interest alongside Newcastle.
Newcastle are prepared to go as high as £40m for Trafford, who cost City an initial £27m last summer, but Manchester City are believed to be holding out for closer to £50m.
Trafford has told his camp he did not want to discuss his future until after the World Cup, and with Newcastle having missed out on him twice before and any deal described as "complex", the club are also exploring other options, including Parma goalkeeper Zion Suzuki and Brighton's Carl Rushworth, who Newcastle scouted last season during his promotion-winning loan spell at Coventry City.