The full-back completed a move to Barcelona on Wednesday.
Digne officially joined the La Liga club on Wednesday as they completed a £16.7million move for the full-back.
The Reds are thought to be in the market for a new left back this summer after Alberto Moreno continued to struggle last season.
Liverpool were interested in Digne last summer, before he eventually moved on loan to Serie A side Roma, and according to the Mirror they were once again considering signing him this summer as Jurgen Klopp reshapes his squad.
Indeed, they report that they made an enquiry for his services but were not quick enough and eventually lost out to Barcelona.
They also claim that the Reds could have secured the Frenchman for less than the €20 million (£16.8m) that the La Liga champions have ended up paying for him.
The Reds did not make their move though and instead Luis Enrique’s side stole a march and secured his signature.
Klopp must now turn his attention elsewhere, and perhaps missing out on Digne will lead to him firming up his interest in Leicester City’s Ben Chilwell.