The Real Madrid star's participation in Brazil was put in jeopardy in mid-November when he suffered a serious knee injury in Germany's 1-1 friendly draw with Italy.
Khedira, 26 and a key figure in the German teams that reached the semi-finals in both the 2010 World Cup and UEFA EURO 2012, underwent surgery to repair the ruptured anterior cruciate ligament in his right knee.
Low, giving an update on Khedira's fitness, told German newspaper Bild: "I spoke by phone with Sami three days ago, he's feeling fine, working a little on the treadmill and isn't feeling any bad reaction."
The Germany coach added: "There's no fixed date, but clearly we are going to have to see in April what form the players are in."
He warned that it would be difficult to pick a player "who hasn't played in a competitive match". Germany are in Group G at the World Cup against Portugal, Ghana and the United States.