Jones made it 100 Reds appearances in all competitions, having made his debut under the German former coach.
Klopp was happy to congratulate his former player, as he watches his old club top the Premier League under new boss Arne Slot.
Jones told Match of the Day: "I came in then and normally text family and I saw a text off (Jurgen) Klopp saying 'congratulations on 100 games and here’s to 500'. I was like what is he on about?'
“I just checked then and I am proud. It was him who set up the team we have now. The foundation was there and Arne Slot has carried it on.
“It looks good but there are plenty of games to come. You can play a team at the bottom, middle or top and it is a hard game. It is about trying to win every single game and if we do that everybody knows what comes at the end.”