The Sun's Goals pullout (page 7 Saturday May 19) reports both West Ham and Leicester are both keen on the Egyptian defender.
Hegazi is available for just £2.5 million due to a relegation release clause in his contract.
This makes it very difficult for West Brom to hang onto the defender, who they signed just last summer.
Hegazi is in Egypt's squad for the World Cup and has a chance to bolster his reputation.
This also makes it smart for either West Ham or Leicester to try and get a deal done now, before more clubs enter the fray.
Hegazi is certainly worth a gamble for either West Ham or Leicester, who are both looking to replace centre-backs.
West Ham have let veteran James Collins go while Leicester are set to part ways with Robert Huth.