Gimenez has spoken about what this means to him during a media appearance with the Uruguay national team.
"I treat this with a lot of responsibility, it's a nice responsibility," he said. "It's something that comes naturally when you've been at the club for several years."
Gimenez is also having to get used to leading the back line, now that Diego Godin has departed.
"I try to make the most of this," he said. "I'm trying to keep learning new things.
"This is something I am facing with motivation.
"I want to keep learning, keep growing and become a better player."