Non-profit organisation the Presidium Network is assisting two of the men, charity medic Kevin Cornwell and a second unnamed man.
Presidium confirmed that the third man is Miles Routledge, the British holidaymaker who received widespread attention and criticism on social media in August 2021 having travelled to Afghanistan despite the Taliban’s gains in the nation.
The two men being assisted by Presidium were detained by Taliban secret police on January 11.
It is unclear how long Mr Routledge has been held for.
Speaking on the Sophy Ridge On Sunday programme on Sky News, Home Secretary Suella Braverman said: “Anyone travelling to dangerous parts of the world should take the utmost caution.
“If they are going to do that they should always act on the advice of the Foreign Office travel advice.
“If there are risks to people’s safety, if they’re a British citizen abroad, then the UK Government is going to do whatever it takes to ensure that they’re safe.
“And the Government is in negotiations and working hard to ensure people’s safety is upheld.”
Pressed on whether negotiations are currently happening, Ms Braverman replied: “If there are problems and if there are safety concerns to British individuals abroad then the FCDO will be working actively to ensure people are safe.”
Scott Richards, co-founder of the Presidium Network, who initially spoke to the Mail On Sunday, told the PA news agency on Saturday: “I am told that those men are in good health and being treated well.
“I have no reason to believe they have been subject to any poor treatment whatsoever.”
Mr Richards said the men are being held in a general directorate of intelligence facility for foreigners.
He said there has been no contact with the men.
A Foreign, Commonwealth & Development Office (FCDO) spokesman said: “We are working hard to secure consular contact with British nationals detained in Afghanistan and we are supporting families.”
The FCDO continues to advise against all travel to Afghanistan based on the security risks, including detention.