The Brazilian veteran has been heavily linked with a winter move to Italian side Inter Milan, while homeland outfit Atletico Mineiro are also showing significant interest.
However, Klopp believes the 30-year-old midfielder, who has been operating in defence at times this term, will continue his 10-year association with the Reds.
After Lucas scored his first goal since 2010 to see Liverpool past Plymouth Argyle 1-0 in the FA Cup third-round replay, Klopp was asked if the player would be staying at Anfield this month.
The German said: "I would say yes."
Regarding Lucas' goalscoring exploits, which sent the Reds to the fourth round of the cup, Klopp added: "Every week in training we play old versus young and he is a top scorer for old, which is unbelievable."