It has been widely reported that the La Liga giants are focusing their attentions on trying to sign Chelsea winger Eden Hazard, but with the Blues not interested in parting ways with the Belgian, they are considering their options.
According to Tuttomercatoweb, that has resulted in an interest being taken in Wijnaldum, who is currently competing in his first season at Anfield.
The 26-year-old has been a regular in Jurgen Klopp's starting lineup this season, contributing five goals and six assists from his 33 appearances, but Real's alleged interest in the player will be regarded as a surprise.
It has been claimed that talks have already been held between Wijnaldum's agent and Real, who appear keen to push through a transfer.
Klopp is unlikely to want to sell the Netherlands international, but it may depend on how much Real are willing to pay for a player who cost £25m last summer.