The Belgian has managed just 15 Premier League appearances for the defending champions this season, while Manchester United have opened up a 12-point lead at the top of the table
Kompany has not featured for the champions since January 26 and has only made 15 appearances in the Premier League this season.
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"But we didn’t think that Vinnie would be out for 45 days. Vinnie has started to run, and we hope and think he’ll be ready for [the game against] Newcastle.
"He [Kompany] started training with us four days ago, but he was tired because he worked a lot. His calf was tired, but it is no problem. We don’t want to take a risk at the moment.
"We have one game then the international break, better that we wait. I don’t think he is out for the season but the calf is a dangerous injury. If you don’t recover well, you can have a problem for four, five, six weeks in a row. After the break, I think he will come back."
The Italian is hoping that leaders Manchester United will drop points between now and the Manchester derby on April 6 as City look to upset the odds and stage a stunning comeback into the title race for a second consecutive season.
"United play at home against Reading and then go to Sunderland," said Mancini.
"We hope we can play the derby with a gap of nine or seven points, certainly less than 12. Because from the derby to the end of the season, United have three or four difficult games."