No, I do not believe this will happen.
Liverpool FC transfer discourse is mostly made up of rumours that mostly pop up to fill whatever obvious need the team has. With Salah and Mane’s impending January absences, that hole is now obviously at the attacking positions, with a winger the ideal solution. The name currently on everyone’s lips, Colombian international and FC Porto star, Luis Diaz. (It’s also sorta amusing that Liverpool is always rumoured to be interested in stars of continental opposition.)
Reports from Jornal de Noticias (Portugal) and AS (Spain) both paint the same picture, with the Reds reportedly looking to sign the South American attacker in the winter transfer window. AS even say that Klopp is pressing to the club sign the winger himself.
A versatile attacker, Diaz can line up on either flank but has mostly flourished at left-winger. He has been in brilliant form this past year, helping Colombia to third place in the Copa America with 4 goals (joint top goalscorer with Messi). In 11 league games so far this season, he scored 9, with another 2 in 4 Champions League appearances.
Here’s why this rumour is unlikely to be true: Diaz reportedly has a clause of €80 million/£67million. I find it very hard to believe that Liverpool would come close to breaking their record fee for a backup to Salah or Mane. A move in January would only make that more expensive.