The French defender, 27, suffered a ruptured cruciate in pre-season training and went under the knife last month.
He has been doing rehab in Italy and Toon chief Rafa Benitez has been keeping tabs on his progress.
He said: "He is getting better – you have his Instagram!
"He will come back maybe in one week He's doing his rehab in Rome, special facilities."
Benitez is unhappy at a lack of summer signings as he tries to keep the Magpies up.
Lejeune's return will be a welcome boost with winless Toon sitting in the drop zone on two points from six matches.
The Magpies host Leicester today and will hope to hit some kind of form.
And Benitez has targeted the Foxes for a first victory after a tricky run of fixtures.
He added: "I am not happy just drawing games. We have to win, and we have to win right now.
"We have to improve in attack – that’s obvious – but I have confidence that the next games against teams not as strong [as the top six], we will have more chances to create something.
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