The pro-Beijing leader has faced sustained criticism from protesters in the semi-autonomous city.
So far the central government in Beijing has given its support to her and the Hong Kong police, calling the demonstrators "rioters" and condemning the violence.
But according to the FT report, which quoted unnamed figures briefed on the deliberations, the Chinese government is drawing up a plan to replace her with an interim chief executive.
However, sources told the newspaper that the plan would be dependent on the situation in the city first stabilising so that Beijing is not seen as giving in to violence.
Lam's office did not immediately respond to a request for comment on the report.
Hong Kong has now been battered by 20 weeks of protests and with no political solution in sight, clashes have intensified each month.
Hong Kong leader apologises for mosque water cannon incident
Earlier this month, Lam - who has refused to grant any major concessions to protesters - invoked a colonial-era emergency law to ban face masks, setting off a new wave of protests and vandalism that shut down much of the city's transport network.
If President Xi Jinping decided to go ahead with the plan to remove Lam, the report said her replacement would be installed by March.
Leading candidates being considered to replace Lam reportedly include Norman Chan, former head of the Hong Kong Monetary Authority, and Henry Tang, who has also served as the territory's financial secretary and chief secretary for administration.
A leaked audio recording emerged in September of Lam saying she would quit if she had a choice - although she later said she had not contemplated standing down.
Lam has faced a series of political difficulties since the city's legislature returned for a new session last week.
She was unable to give her State of the Union-style policy speech after pro-democracy lawmakers repeatedly interrupted her, forcing her to deliver the address via a pre-recorded video.
COMMENTS
Comments are moderated and generally will be posted if they are on-topic and not abusive.
For more information, please see our Comments FAQ