Kante's season has been scourged by injuries that date back to the Europa League final win over Arsenal.
And Lampard is hopeful France will grant Kante the international break to work on his physical condition.
"It is a difficult one. He has had four years of constantly playing," Lampard said.
"[The] injury from the Europa League final has affected his pre-season. Then he hurt himself against Man United.
"We are trying to get him through it. Today was too painful. The international break will be great for him to get the injury right. It would be great for everybody [if Kante stays] because he's been playing game after game after game."