The Germany international turned down a contract extension with Real last year and becomes a free agent this summer.
“Khedira has an interesting profile and not just for us,” Juventus general director Giuseppe Marotta said to the Italian press. “It’s an opportunity because he is out of contract.
“We are thinking about it. We will evaluate the situation in the next few days.”
Juve will face competition from Premier League sides for Khedira’s signature.
Manchester United, Arsenal, Chelsea and Liverpool have all been linked with the highly coveted midfielder as well as Bundesliga outfit Wolfsburg.
Khedira, 28, joined Real Madrid from Stuttgart in 2010 for an undisclosed fee.
A World Cup winner with Germany in 2014, Khedira has made just 11 league appearances for Real this season.
Juve, who will take on Barcelona in the Champions League final on June 6 in Berlin, are also keen to sign Fiorentina goalkeeper Norberto Neto.
The Brazil international turned down a new deal with Fiorentina earlier this year and becomes a free agent next month.
“Neto’s situation is the same as that of Khedira,” Marotta said. “He has done really well this season.”
The 25-year-old is a reported target of Liverpool and Roma and has made 36 starts for Fiorentina in all competitions this season.