Liverpool are considering selling both Loris Karius and Simon Mignolet after the arrival of Alisson, according to the Daily Telegraph.
Karius is reportedly a target for Bayer Leverkusen, while Barcelona and Besiktas are after Mignolet.
Klopp is reportedly happy to sell both goalkeepers, after Alisson arrived for £65m from Roma.
Liverpool are considering signing rookie Barnet goalkeeper Kai McKenzie-Lyle, according to the Daily Mirror.
The 20-year-old stands at 6ft 7in, and made his senior debut in 2015. He was born in Haringey, but has made two appearances for Guyana and was previously at Tottenham at youth level.