According to The Sun, Zakharova is due to undergo surgery, but her operation has been repeatedly delayed.
Despite a local charity, Rainbow of Goodness, also lobbying to have Zakharova allowed to attend the daycare, centre staff have reportedly refused to back down. They claim other children will be scared of her appearance.
Meanwhile, local media report that educational experts are expressing concern for the child's development if she is not allowed to interact with other children.
Educational Psychologist Ekaterina Belan said: "The sooner she gets the experience of interactions, the easier it will be for her to cope with the conditions in which she lives and grows.
"The more interactions she gets, the easier it will be for her to accept herself for who she is."
The Sun also reports that local authorities are investigating both the daycare's rejection and the delays to Zakharova's medical requirements.
Head of the Bashkortostan government, Radiy Khabirov, has advised that legal action will be taken over the violation of the family's rights to access education.