Arsenal boss Arsene Wenger had made signing a new centre-half a priority for the January market.
The Daily Mail says Arsenal will discuss their defensive options during a scouting meeting this week.
Celtic's Virgil van Dijk, West Ham's Winston Reid, Aston Villa's Ron Vlaar and Manchester United's Chris Smalling were all considered in the summer.
Vlaar and Reid could both be available in cut-price deals because their contracts expire at the end of the season.
