After helping Liverpool win the Champions League, Mane guided Senegal to the Africa Cup of Nations final in Egypt, where it lost to Algeria in the decider.
The attacker's busy off-season will mean he misses the Community Shield on August 4, set to return just four days out from his side's league opener against Norwich City.
"He is in good shape," Klopp said.
"Obviously they had a celebration in Senegal and I'm happy about that because it showed that they respect the competition and saw the second place as a success, which is nice.
"He is now on holiday, not the longest one. He will be back on August 5, after the Manchester City game. That means he had two weeks.
"There is four or five days to prepare for Norwich, 10 days for Chelsea [in the UEFA Super Cup]."
Mane scored 26 goals in 50 games in all competitions for Liverpool last season.