According to The Chronicle, Rafael Benitez attempted a late swoop for Klavan in an attempt to appease Newcastle fans who have been frustrated with a lack of ambition from their club to strengthen the squad ahead of the new campaign.
Klavan has fallen down the pecking order at Anfield this summer, competing for minutes with Virgil van Dijk and Dejan Lovren. The Estonian failed to make the squad for Liverpool's opener at home to West Ham United.
Although Newcastle were reportedly keen to make a deal happen, it is believed Jurgen Klopp wanted to keep the 32-year-old centre back as the Reds' boss fears over the depth of his squad.
Liverpool's defence under Klopp is an area that has come under great scrutiny, with Klavan being one of the defenders who featured regularly. The £75m signing of Van Dijk in January has since limited the Estonian's playing time and will likely have to settle for outings in the Carabao and FA Cup ties.
Since joining from Augsburg in July 2016, Klavan has shown moments of promise to implement himself into Liverpool's back four. Though lapses in concentration have brought concerns to the Liverpool faithful, holding him back from becoming a stalwart in the starting lineup.
Making 39 Premier League appearances over two seasons at Merseyside, Klopp apparently still believes that Klavan has a place in the roster for what promises to be an exciting season.