Mane will in my opinion not be available until last week of August, or possibly first week of September.
Consider that Liverpool's season finished on 1st June 2019. At most he will have had 10 days rest before joining up with the Senegal squad for the ACON and maybe there until the 19th July 2019. He'll need rest and recuperation. A months break minimum, probably longer, and then a short training stint before he can play again.
If Liverpool don't give him a rest, they will risk fatigue and injury.
We'll have a similar problem but to a smaller extent with Mahrez. Smaller because City's season ended earlier and Mahrez did not play as much in 2018/19.