The Magpies confirmed their first addition of the summer on Friday night, with Anthony Elanga having finalised his move from Nottingham Forest.
Newcastle are paying an up-front fee of around £52m to sign Elanga, with a further £3m of potential add-ons also also agreed.
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Newcastle’s recruitment team are also hoping to have Trafford on board by the time Eddie Howe takes his side to Parkhead for their opening friendly against Celtic next weekend, with talks over the goalkeeper set to spark back into life.
The Magpies’ initial bid of around £27m was rejected earlier this summer, with Burnley holding out for a higher fee for the 22-year-old, who is set to leave Turf Moor despite the Clarets winning promotion last season.
It has been suggested that Burnley are holding out for a £40m deal, and while Newcastle will not be offering that figure in an up-front fee, they are understood to be preparing a package that could come close to reaching that sum if a series of add-ons are triggered.
The expectation is that if Trafford signs, he will compete with Nick Pope for a starting spot next season, with Pope having signalled his desire to remain at St James’ Park no matter what happens in terms of an incoming.
Newcastle are also keen to sign a centre-half this summer, with Atalanta’s £50m-rated Giorgio Scalvini still of considerable interest, and a forward to replace Callum Wilson, whose departure as a free agent following the end of his previous contract was confirmed earlier this week.