Paris Saint Germain left-back Dani Alves is a free-agent this summer
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The Reds are still out in the market in search for an adequate left-back to replace Alberto Moreno and provide backup for Andy Robertson next season.
Moreno couldn't make it into Jurgen Klopp's defensive plan since the arrival of Robertson in 2017.
The Spaniard has now been shown the exit door this summer and a replacement for that role is in no doubt a must for the Reds.
Former Manchester United player Kleberson believe Dani Alves would provide - a suitable alternative for Jurgen Klopp's left-back position next season.
The former midfield player said: "I wanted to get Dani Alves to join me in the MLS. He's a phenomenal player with amazing quality.
"I feel maybe could fit in well at Liverpool and Klopp would like him as a style of player. He's very technical, fast and has an incredible temperament in the big games. He's a winner"
Kleberson won the World Cup with Brazil in South Korea and Japan in 2002, and played alongside the former Barcelona full-back [Dani Alves] between 2006-10 for the Selecao.