The newspaper is a competitor of London Lite
, published by Associated Newspapers. It has lost £12.9 million ($21.2 million) in the year up until June.
News International will discuss with staff the possibility of closing.
It was only recently that Rupert Murdoch, who is chairman of the parent company News Corporation said it would introduce charges for reading newspapers online.
Lorna Tilbian, a media analyst at Numis Securities told the BBC, "You can't give it away on the streets and then start charging for it online."
She also said that was only enough space for one free paper in the London area
The London Paper was first published in 2006 and last months circulation was more than 500,000 copies but News Corporation would now like to focus on its other newspapers such as The Sun
and News of the World
James Murdoch from the News Corporation said to the BBC, "The strategy at News International over the past 18 months has been to streamline our operations and focus investment on our core titles. The team at The London Paper has made great strides in a short space of time with innovative design and a fresh approach but the performance of the business in a difficult free evening newspaper sector has fallen short of expectations. We have taken a tough decision that reflects our priorities as a business