The 29-year-old midfielder suffered a thigh injury while on international duty in last month's 1-1 draw with Italy.
"We travelled with the Real physician to Munich to see Dr Wolfhart-Muller, to get a second opinion on the injury," Kovac told Goal.com.
"He has confirmed what we had pointed out to the club. It's a pretty serious problem but his recovery is developing well and we hope to see him back on the field in March.
"This injury has been caused by the large number of games he has played. I've been a footballer and have played two and three times a week, and it's very hard."
Real coach Carlo Ancelotti issued his own update on Modric's situation on Thursday.
He told AS: "Until now he's been having physiotherapy. His scars are healing well.
"Things have gone well until now. He won't be back soon, but he will start training in the middle of January."
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