Words by ITV News Multimedia Producer Wedaeli Chibelushi
The proposal, announced on Thursday, has been widely condemned by charities and campaign groups on the grounds of human rights - with others raising issues around cost and effectiveness.
Among the critics is Rainbow Migration, a non-profit that guides LGBT+ people through Britain's immigration system.
In a statement, it said the Rwanda policy was "extremely concerning" as there is "widespread evidence" of LGBT+ discrimination in the east African country.
Although homosexuality is legal in Rwanda, it remains a taboo.
The UK government's own web page with information about travelling to the country states "LGBT individuals can experience discrimination and abuse, including from local authorities".
Gov.uk also acknowledges that no specific anti-discrimination laws protect LGBT+ individuals in Rwanda.
For analysis on news' biggest stories, listen to the ITV News What You Need To Know podcast
Rainbow Migration said: "The situation for LGBTQI+ people in Rwanda is so poor that it is a source country for people seeking asylum in the UK based on their sexual orientation, albeit in low numbers, and we have previously provided support to LGBTQI+ people from Rwanda."
The LGBT+ group at Unison, one of the UK's largest trade unions, shared Rainbow Migration's sentiments.
"Rwanda is not safe for LGBT+ asylum seekers. Another shameful decision by the UK government," the group tweeted on Thursday.
The plan was also slammed as an "attack" on the LGBT+ community.
Jayne Ozanne, a campaigner and a former government LGBT+ advisor, said: "You finally flee to UK as a gay single man and you get sent back to... Rwanda."
The Rwanda policy would only apply to single, male asylum seekers, the government briefed on Thursday.
In response to ITV News, the Home Office said: "Rwanda is more progressive on LGBT+ issues than other countries in the region. Its legislation does not criminalise sexual orientation or consensual same-sex acts between adults.
"Rwanda has held a successful Pride event in its capital and is making progress in its attitude affecting LGBT+ people. Its constitution outlaws all discrimination. The British High Commission meets regularly with LGBT+ activists in Rwanda and discusses LGBT+ rights with the government of Rwanda."