Dejan Lovren returned to training on Monday to hand manager Jurgen Klopp a boost ahead of the Premier League opener against West Ham on Sunday.
Injuries to Klavan and Matip had left Klopp with only two fit central defenders for the game against Napoli over the weekend, but Lovren's return to the fold gives the German an additional option for Sunday's match.
The Croatian was pictured doing fitness work at the club's Melwood training base on his first day back from holiday after the World Cup.
In a video on Liverpool's social media channels, the centre-back could be seen doing squats and stretches in the gym as he began his pre-season fitness work.
The 29-year-old could come into contention for Liverpool's final pre-season fixture against Torino on Tuesday, with Virgil van Dijk and Joe Gomez the only senior centre-backs currently fit and available.
Earlier on Monday, Klopp had admitted concerns over his defensive options as Matip (hip) and Klavan (hamstring) both remain doubtful for the matches against Torino and West Ham.
'Joel, we'll have to see. Klavan, shouldn't be too serious, but if Tuesday is too early I don't know yet,' Klopp told the Liverpool Echo.
'Maybe we will do some magic things with the formation on Tuesday. I don't know how we will do it.'
Liverpool, who have been tipped by many to mount a title challenge this season, have splashed the cash this summer in an attempt to close the gap on champions Manchester City.
Brazil international Alisson arrived from Roma in a world record deal for a goalkeeper, while Naby Keita, Fabinho and Xherdan Shaqiri have also joined during the close season.
After Sunday's clash with fellow big spenders West Ham, Klopp's side then face Crystal Palace in London on August 20 and Brighton at Anfield five days later.