Hughes is thought to be keen to bolster his defensive options with new full-backs believed to be his top priority.
Osasuna are keen to keep the pair and club president Patxi Izco insists they would only consider selling the duo if someone meets their buy-out clauses.
"There is nothing to discuss or negotiate," Izco told Diario de Noticias de Navarra.
"We rely on both players and they can leave the club in January only if will come some club who pay their clauses."
Azpilicueta is understood have a release clause of £13.5m while in the case of Monreal it is of £10.8m.