According to German daily Bild, Kimmich is one of five Bayern players who are unvaccinated.
After playing in Saturday's 4-0 win at home to Hoffenheim which kept Bayern top of the Bundesliga, the 26-year-old told Sky he has reservations about getting vaccinated, "especially with regard to the lack of long-term studies". Even though he has so far refused, Kimmich said he is "aware of his responsibility. I stick to the hygiene measures and get tested every two or three days. Everyone should make the decision for themselves."
The German international insists he is not opposed to people getting the vaccination and with numbers of new cases currently rising in Germany, it is "very possible that I will get vaccinated soon. It's simply that I still have some concerns."
Before kick-off on Saturday, Bayern sports director Hasan Salihamidzic said the club "recommends its employees get vaccinated in order so everyone can have a more normal life again. "But in Germany one doesn't have to be vaccinated. Every employee can decide for himself."
Nagelsmann missed Saturday's match after testing positive for Covid-19 in midweek. Alongside the head coach, Kimmich's team-mates Serge Gnabry, Thomas Mueller, Benjamin Pavard and Leon Goretzka have all tested positive for the virus over the last 12 months.
Currently, Bayern pay to have their players tested regularly. "If that was no longer the case, I would do it (pay) myself," said Kimmich.
Last year, Kimmich and Goretzka founded the initiative "We kick Corona" by donating money to support vaccination campaigns and charitable projects.
Germany's seven-day coronavirus incidence rate reached 100 infections per 100,000 people on Saturday for the first time since May, following a surge in cases in recent weeks. More than 66 percent of the population of Germany, a country of some 83 million people, is fully vaccinated against Covid.
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