Kulikov was born in Moscow and started playing football at the team, called Prialit. Later Daniil had a successful trial at the Lokomotiv Academy, but a year later he was sent to Lokomotiv-2, where he played until graduation. Kulikov did not manage to get into the youth team straight away - he had to play in KFK, where he was noticed by the coaches of the youth team Denis Klyuev and Ansar Ayupov, who called him to the training camp.

In 2016, Kulikov, together with the youth team, won the Russian championship, in 2017 he went to the training camp with the main team for the first time, in 2018 he made his debut for Lokomotiv, in 2019 he won the Russian Cup and the Super Cup.