The hearing will be Watson's sixth since his arrest in July in Nuuk, capital of the Danish autonomous territory.
Prosecutor Mariam Khalil told AFP that she has "requested a four-week extension to the period of pre-trial detention".
Watson's lawyer Julie Stage is meanwhile pleading for his release.
"I'm going to ask for his immediate release," she said.
The activist, who turns 74 on Monday, was detained on a 2012 Japanese arrest warrant, which accuses him of causing damage to a whaling ship in the Antarctic in 2010 and injuring a whaler.
Watson, who featured in the reality TV series "Whale Wars", founded Sea Shepherd and the Captain Paul Watson Foundation (CPWF) and is known for radical tactics including confrontations with whaling ships at sea.
"It's absurd. Every time it's the same thing, we wonder why they even convene the hearing," Lamya Essemlali, President of Sea Shepherd France, told AFP.
Watson was arrested on July 21 when his ship, the John Paul DeJoria, docked to refuel in Nuuk on its way to "intercept" a new Japanese whaling factory vessel in the North Pacific, according to the CPWF.
Decision pending
The Danish justice ministry, which has consulted with Greenland police and the Danish prosecutor general on the case, told AFP over the weekend that it was nearing a decision on the matter.
"The Danish Ministry of Justice is currently processing the extradition request... expecting to soon make a decision," it said in a statement.
In late November, Watson's lawyers urged Danish Justice Minister Peter Hummelgaard to block the extradition.
If Denmark refuses his extradition, "there would no longer be any reason for detention and (Watson) would be released as soon as possible," Khalil explained to AFP in November.
If Denmark were to agree to Japan's extradition request, Watson's lawyers would lodge an appeal.
According to Stage, the decision should be made "within 14 days".
Tokyo accuses Watson of injuring a Japanese crew member with a stink bomb intended to disrupt the whalers' activities during a Sea Shepherd clash with the Shonan Maru 2 vessel in 2010.
Watson's lawyers insist he is innocent and say they have video footage proving the crew member was not on deck when the stink bomb was thrown. The Nuuk court has refused to view the video.
In September, Watson's lawyers contacted the UN special rapporteur on environmental defenders, claiming that he could be "subjected to inhumane treatment" in Japanese prisons.
The defence team has argued that the crime of which Japan accuses him does not even carry a jail sentence in Greenland, a point on which the prosecution disagrees.
In a rare public comment on the case, Japan's Foreign Minister Takeshi Iwaya has said that the extradition request was "an issue of law enforcement at sea rather than a whaling issue".
Watson hopes to be freed to return to France, where he had been living since July 2023 and where his two young children attend school.
He requested French citizenship in October.
Watson's legal woes have attracted support from members of the public and activists, including prominent British conservationist Jane Goodall, who has urged French President Emmanuel Macron to grant him political asylum.
A petition for his release has gathered 210,000 signatures, and some 220,000 have signed in support of his application for French citizenship.
