The 32-year-old, who joined the Blues on a one-year contract last summer, has been recently linked with his former clubs Barcelona and Inter Milan.
"False and degrading information has been published about me," the forward posted on Instagram.
"I just want to remind to all that I have a tremendous love for Chelsea. I have a lot of respect for my leaders and teammates.
"I love Chelsea fans and I will keep on giving everything I have to defend the Blues."
Eto'o has scored eight goals in 27 games for Chelsea so far this season.