Vardy was sent off in the second game of the season, incurring a three match ban.
But he will be free to play in the clash against Bournemouth after the international break.
And the English striker, who retired from the national team, is ready according to his manager.
"It will be important to have Jamie back," said Puel to Leicestershire Live.
"We have been working to maintain him at a good level without a game and he can do a good training session with good intensity because perhaps he will play without games for four weeks.
"That is a long time. I hope he can come back with a good fitness but I am sure about his mentality. I want him to maintain a good level of fitness.
"He was frustrated but he kept smiling and he is always a good team-mate in training.
"He is happy about the quality on the pitch of the team."