Carmo, 22, is having a fantastic campaign in Portugal, and according to the report, Klopp has recommended the Braga centre-back to the Reds' transfer committee as he looks to build after signing a new deal.
The player, who has a €40million (£34m) release clause, nearly joined Klopp’s side 18 months ago, at a time when Braga’s president Antonio Salvador believed a move to Merseyside would probably happen.
Speaking in April 2021, he said: “We have kept it as long as possible, but every year we have to sell. In January, David Carmo had a foot and a half at Liverpool, but we ended up retaining him.
“He is a player who, despite being injured at the moment, continues to have several suitors, even in Spain. To have a balanced budget, we have to receive between €12.5m and €15m a year in transfers.
“This is an established point if we are to continue at the same level that we have been at for the last decade. This year we will have to do more to resist the damage caused by the pandemic.”
Despite a deal never coming to fruition, it looks as though the Portuguese defender could be heading to Anfield in the near future.
A physically imposing centre-back, Carmo has previously been dubbed ‘the new Sergio Ramos’ by his former youth coach Jose Carvalho Araujo.
“He is a player with a voice. He knows what he has to do on the pitch. I remember that at the beginning he was an introvert, but he was young. In the under-23s, he was already admired for being a leader and for everything he had achieved,” Araujo said.
“He is one of those players who creates a good atmosphere in the dressing room. He may not yet be as charismatic as Sergio Ramos, but he could be with age.”
Despite the comments, it remains to be seen where he would fit in given the Reds are well-stocked in defence.
Virgil van Dijk continues to be a colossus at the back, and Joel Matip’s reputation has skyrocketed after impressing alongside the Dutchman.
Liverpool also moved swiftly to secure the services of Ibrahim Konate from RB Leipzig last summer, and have Joe Gomez as backup if required.
Gomez, however, has seen game time limited this season, and continues to be linked with a move to both Newcastle and Aston Villa.
Youngsters Rhys Williams and Sepp Van den Berg are likely to leave on-loan at the end of the current campaign, and Ben Davies and Nathaniel Phillips are expected be sold permanently.
The Reds, meanwhile, are no strangers when it comes to scouring the Portuguese market. They secured the services of Luis Diaz in January from Porto, and could now turn their attentions to Carmo.