Manager Mauricio Pochettino confirmed on Thursday that the French goalkeeper will remain Spurs skipper, despite being fined £50,000 and banned from driving for 20 months after being caught more than twice over the legal limit.
Tottenham are also understood to have fined the World Cup winner £250,000, which is the equivalent of two weeks' wages, and warned him about his future conduct.
Some have questioned why Lloris has kept hold of the captain's armband, though, having endangered the lives of others with last month's antics.
The Sun reports that the 31-year-old was willing to quit his role as leader of the team, but Pochettino does not see the need for change.
Lloris will miss "several weeks" of action with a thigh injury.