Motivated by recent attempts to study the implications of Tsallis and Rényi statistics in gravitational, cosmological, and astrophysical systems, the possible relationships between 𝐻0 tension and generalized statistics are explored. It is obtained that, in the light of 𝐻0 tension, the energy-time uncertainty relations in Tsallis and Rényi statistics constrain the values of Tsallis and Rényi parameters. Hence, the way to find the footprints of non-extensivity in the universe is paved.
