The Sun says the Gunners are leading the race for the England winger ahead of rivals Manchester United and Liverpool.
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Arsenal are prepared to pay £75m to ferry the Scouser from Newcastle to London.
For their part, Newcastle price Gordon at £100m, though there is a belief inside Arsenal that the Toon will compromise, particularly if Gordon makes it clear he wants the deal to happen.
Gunners manager Mikel Arteta is a fan of Gordon and appreciates his versatility, knowing the winger can comfortably play centrally as a striker when needed.
Any deal for Gordon is likely to see Arsenal encourage offers for Gabriel Martinelli over the summer.
