Liverpool have had a bid of around £4.2m accepted by Klavan's current club, Bundesliga side FC Augsburg.
Klavan is predominantly a left-sided centre-back so will act as cover for the injured Sakho but he's also capable of playing at left-back if required so he'll give Klopp another option behind Alberto Moreno. With Kolo Toure and Martin Skrtel sold, as well as Tiago Ilori on global duty for the beginning of the season, he'll give Klopp an experienced player to slot alongside either Dejan Lovren or Joel Matip as needed. According to widespread reports, the club have joined the race for Wijnaldum.
Klavan, an Estonia global who has been capped 108 times, is a player whom Klopp knows well from his time in the Bundesliga, given he has played for Augsburg since 2012.
Adding to that, young Joe Gomez is set to miss the start of the season following suffering a setback in his recovery from a long term injury, whilst Mamadou Sakho too is a doubt for the opening weeks.
Wijnaldum moved to Newcastle at the beginning of last season for a fee of £14.5 million.
Dutch midfielder Georginio Wiljnaldum is on course for a possible move to Liverpool from relegated Newcastle United.
Jurgen Klopp is now short of options at the back.
As soon as news broke of Liverpool's interest in Klavan on Sunday evening, reports of another transfer emerged.
His pursuit of Piotr Zelinski, the Udinese midfielder, has also floundered after the Italian club refused to sell him to Liverpool, even though the Poland worldwide wanted to move to Anfield.
Liverpool is one of the most successful football clubs in the world, having won 18 English League titles.