With Real set to trigger the buy-back option in the contract of Eintracht midfielder Omar Mascarell, the Germans want the LaLiga giants to provide a replacement.
And Llorente has been requested by Eintracht chiefs.
However, Don Balon says Real have asked Eintracht to be patient with the future of Llorente still being considered.
The midfielder is unhappy at Real and wants to leave, but management are reluctant to cut him loose outright. Keeping hold of Llorente also still hasn't been ruled out.