The Germany international, who has previously been linked with Manchester United, Arsenal and Chelsea, will see his current deal with Juventus expire at the end of next season.
The 31-year-old has insisted that he is "fine in Turin", but suggested that he wants to play in England before hanging up his boots.
"My contract expires in a year. I often think of the future because anything can happen. I'm fine here, but I love challenges and I look for them," Khedira told Bild.
"I would like to win as many titles as possible in as many championships as possible. Among the best leagues in Europe I lack England, having won in Spain, Germany and Italy.
"The Premier League has always fascinated me. Winning the title there would complete my collection. But I do not want to nominate or propose: I'm fine in Turin and predicting the future in football is difficult."
Khedira has won league titles in Germany, Spain and Italy.