The Brazilian defender is available on a free transfer this summer following two seasons at Ligue 1 side Paris Saint-Germain.
The 36-year-old has been linked with a potential return to FC Barcelona despite leaving the La Liga side in 2016.
Alves was named the Copa America player of the tournament as Brazil won the trophy this summer.
Liverpool FC already have Trent Alexander-Arnold, who has impressed in a right-back role over the past two seasons.
But former Man United midfielder Kleberson believes Alves would be a shrewd addition to the Liverpool FC team ahead of the new season.
“I wanted to get Dani Alves to join me in the MLS! He’s a phenomenal player with amazing quality,” Kleberson told YourPromotionalcode.co.uk.
“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.”
Alves has been a serial winner throughout his professional career.
The Brazilian defender won six La Liga titles, the Copa del Rey five times, the Champions League three times and the Uefa Cup twice during stints at Sevilla and FC Barcelona.
Alves won the Serie A crown and the Coppa Italia during the 2016-17 season at Juventus before back-to-back triumphs in Ligue 1 with PSG.
The veteran defender would be joining the best defence in the Premier League if a move came to fruition after Liverpool FC conceded just 22 times in 38 games last term.
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