According to TuttoMercatoWeb, Liverpool's hierarchy are working on a formal proposal that could be submitted during the winter transfer window. The offer is expected to exceed €50 million, with Monaco likely to demand a significant fee before considering his departure.
Camara has become an attractive option after impressing in Ligue 1, and his potential move to England would represent another step forward in his career.
Liverpool are not the only club to have shown an interest. Chelsea previously pursued the midfielder but appear to have moved on, with the London club now reportedly focusing their attention on Bournemouth's Alex Scott.
That could leave Liverpool with a clearer path towards an agreement, although Monaco will still have a major say in the outcome.
The French club are understood to value Camara highly, while the player is reportedly keen to test himself in the Premier League.
Liverpool's interest comes as they consider how best to strengthen their midfield ahead of the second half of the season. A move for Camara would represent a substantial investment, but the club appear prepared to make a significant offer to secure his services.
No agreement has been reached, and Monaco have yet to accept a proposal. However, Liverpool's reported preparations suggest the Senegal international could become one of the names to watch when the January window opens.