Speculation that the mega-rich Ligue 1 side are preparing a swoop for the Danish international has increased in recent days, with some reports claiming a £20m offer is being prepared.
Despite suggestions that this figure may be enough to tempt the Merseysiders into selling their centre-half, Brendan Rodgers is keen to keep him and will reject any advances.
The 28-year-old was rumoured to have been close to joining Manchester City last summer, but elected to stay with Liverpool and has enjoyed a relatively successful season.
Rodgers sees Agger as a key member of his current squad, and somebody that may play a key role in his hopes of Champions League qualification.
Furthermore, with Martin Skrtel looking likely to move on, as well as Jamie Carragher having retired, the Northern Irishman is short on defensive options.
A deal for Kolo Toure has already been agreed, and the Reds are said to be chasing both Kyriakos Papadopoulos and Tiago Ilori, of Schalke and Sporting Lisbon respectively.
Monaco have already been very active in the transfer market, with deals for Radamel Falcao, Joao Moutinho, James Rodriguez and Ricardo Carvalho having been agreed.