The 25-year-old suffered his second serious facial injury in the space of two years in a training-ground clash with team-mate Tal Ben-Haim on Sunday.
"I hope I will be back in the goal soon," said Cech, who hopes the timescale outlined by his coach proves accurate.
"I will have to wait for what the doctor says," added the Czech international.
"I cannot do anything right now, two days after the anaesthetic. The club said I should be back in two weeks, so we shall see. I believe it will be so."
Some reports suggested the treatment could continue for as long as six months and Cech admitted: "If I were a normal patient, it could be like that.
"But as I have to play football, we are trying to find a way to protect the wound - to be back as soon as possible.
"My face is sewn, so we must find a way to protect it from tearing again.
"Once this problem is solved I will restart training. But how long it will take, I do not know."