The 17 year-old is also a target for Liverpool, but the Gunners are now leading the race for his signature, says The Sun.
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Wright has already scored four times for Salford in pre-season.
Liverpool offered £100,000 plus add-ons for Wright, who has made four senior appearances for the Ammies.
But Arsenal have now upped the ante by offering £250,000 plus bonuses for the teen.
Wright, standing at 6ft 3in, was signed two years ago after starring for local teams Euxton Villa and Fylde.