Spanish football expert, Guillem Balague, claims the La Liga club are getting impatient about the transfer and want to force the move.
Liverpool rejected a third bid that adds up to £113m for Coutinho on Friday afternoon and insist they have no intention of selling the 25-year-old this summer.
Balague claims Barcelona have now issued the Reds a deadline of 7pm on Sunday, to accept their latest offer.
“We reported on Friday that Liverpool had rejected the third offer from Barcelona and an email was sent back [to Liverpool] from Barcelona saying, ‘okay, you rejected that – if you don’t accept it I must tell you that there is a deadline of today, Sunday – 7pm. Otherwise we withdraw the offer’.
“I think Liverpool have got no intention of answering that email from Barcelona, which in theory means that’s the end of that.
“That’s the end of the story of Coutinho moving to Barcelona. You never know in football of course but if Barcelona are true to their word they will withdraw the offer tonight because Liverpool have got no intention of selling,” he said.