The England international is ready to leave the Gunners after losing his first-choice status to David Raya.
A move to the Magpies was mooted for Ramsdale, but Newcastle have found his 30m asking price too steep, says the Daily Mail.
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With FFP concerns looming, Newcastle are now seeking a cheaper alternative.
Meanwhile, Ramsdale is also courting interest from Chelsea with the summer market now swinging open.