The Mirror says Lovren looks to have deleted the word 'Liverpool' from his Instagram bio, removed his profile picture and disabled comments on his account.
The Croatian defender had a game to forget against Spurs at Wembley Stadium, and was at fault for their second goal in the 4-1 defeat.
Former Manchester United goalkeeper Peter Schmeichel leaped to the defence of the centre-back on Super Sport, saying: "It's very important to underline that he [Klopp] never ever said anything to him [Lovren] and he's killed that player.
"And in fact it hasn't helped, they are still defending like it's their first time ever. The way they defend today and have been defending all season is so naive and Jurgen Klopp needs to take responsibility."
"What he's done now is put all the responsibility over to Lovren. He will now be in the headlines for this, and that's really unfair. That should be the manager."