Mourinho has long valued a box-to-box type of midfielder, marking his first stint at Chelsea with the capture of Michael Essien, whom he later took to Madrid.
Now Cross reports Mourinho will look to Khedira to fill such a role at Stamford Bridge, although Chelsea may be put off by a £20 million price tag on the German international.
Aiding the Blues’ pursuit is Madrid’s recent acquisition of Asier Illarramendi, who arrived at the Bernabeu from Real Sociedad for £34 million.
The Spanish giants now hope to add Tottenham’s Gareth Bale to their squad for a fee in the region of £95 million, although that figure could rise as high as £125 million.
A sale of Khedira would boost the Bernabeu coffers, and Sevilla midfielder Geoffrey Kondogbia has already been linked as a replacement to boost Madrid’s midfield numbers.
Mourinho had previously said Wayne Rooney was his only transfer target, but Chelsea are ready to offer Khedira a financial package of £4 million per year to bring him to West London.
The German joined Madrid in 2010 and has won Bundesliga and La Liga titles in a career yielding 39 caps.