Khedira has won a growing band of admirers for his performances in South Africa and his club Werder Bremen could be ready to cash in on him at the end of the finals.
The 23-year-old is rated in the £12 million-bracket but he only has one year left on his contract and Werder risk losing him for nothing if they don't sell him this summer.
Manchester United are also keen on signing Khedira as a replacement for veteran midfielder Paul Scholes but Chelsea appear to be in pole position as Ancelotti searches for a replacement for his compatriot Michael Ballack.
Werder Bremen manager Christian Gross admitted to The Sun: "It would be very painful if Sami left on a free.
"If he has two more great World Cup games, all the big clubs will come for him."
Ancelotti has already completed one deal this summer, finalising a £5.5 million move for Liverpool's Yossi Benayoun last week.