ABC says Real president Florentino Perez is inviting offers for both players at a starting price of €50m each.
Odegaard spent part of last season on-loan at Arsenal and the Gunners remain interested.
Mendy, meanwhile, is available with Real management going with captain Marcelo and Castilla prospect Miguel Gutierrez as their new season left-back options.
Inter Milan are among clubs interested in the France international.
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