The Sun says Wolves want Ramsdale as a replacement for Jose Sa, who has offers from the Saudi Pro League.
Ramsdale tops Wolves' list of replacements, with Liverpool's Caiomhin Kelleher also under consideration.
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England international Ramsdale has made just six Premier League appearances this term after losing his place at Arsenal to David Raya.
Raya will sign permanently for the Gunners from Brentford this summer.