The Dutch defender, now 35 years old, will see his Liverpool contract expire next summer as reports claim that talks are ongoing in the background with him and Alisson Becker, who is in a similar situation.
Signed in January and July of 2018 for respective fees of £75m and £65m, both players could leave for free if the Reds do not lock the pair down to fresh terms.
Van Dijk and Alisson could sign pre-contract agreements with overseas clubs in just 51 days and speaking with Hajper, Lovren revealed that all things come to an end as Van Dijk nears the exit.
"It will be strange when Virgil van Dijk leaves Liverpool, but at some point it has to come to an end.
"It’ll be important for him, the fans and the club that he leaves at the right time, if he stays at his level then you can see a one-year extension, but of course he’ll have to keep proving that on the pitch.
"But saying that it’s so important that he gets a good farewell, he deserves it for what he has given to the club for so long, year after year. He has been at the very top.
"He is without doubt one of Liverpool’s greatest ever players. You just need to look at the stats. Look at what he achieved and what he won, it speaks for itself.
"How many times was he up for the Ballon d'Or or in the FIFPro World 11? It’s not just Liverpool, he's top of the tree."
Van Dijk has since been linked with Real Madrid and AC Milan over the past few months and with the Liverpool captain turning 36 next summer, his age clearly isn't a barrier.
The iconic defender reportedly wants to stay, but talks are not being rushed at the moment. However, with January approaching, the side run the risk of losing him for free.