The 32-year-old Estonian was a target for former Liverpool manager Rafa Benitez but Klopp did not want to sell the central defender, according to the report.
Klavan played 26 games for us in the Premier League and the Champions League last season and even scored a goal.
It is a good move by Klopp to not let the Estonian leave as Dejan Lovren now has an injury (h/t Express) and it is unsure as to how long he might be out for.
Liverpool do have their problems in the heart of the defence as Joel Matip too picked up an injury during pre-season and we might be stretched a bit when it comes to the defence.
While Klavan is not at the same level as Van Dijk, he could do a quality job for us when we have to play some of the cup games.
With us having some really poor luck with injuries, we will need Klavan this season for sure.