The Uruguay international, after not seeing eye-to-eye with former coach Xabi Alonso, has produced career best fom under Alvaro Arbeloa this season.
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Sports Illustrated says Valverde's impact has led clubs in Saudi Arabia now readying offers ahead of the close-season market.
Specifically, Al-Ahli is prepared to make a significant financial outlay to sign the midfielder.
Despite this, Real Madrid has made it clear that "El Halcón" is not for sale as his long-term presence is a priority. Real management see Valverde as a midfielder who sets the pace for the Merengues.