Westminster City Council will ask for money from the publishers of free newspapers to deal with the cost of cleaning up discarded copies.
The council says free papers are creating enormous waste
Since the introduction of London Lite and thelondonpaper, the city council says it has to collect an extra 1,000 tonnes of paper a year.
It says distribution has overwhelmed waste collectors and wants publishers to help foot the bill.
News International, thelondonpaper's owner, said it was in negotiations.
West End litter
The council says most copies are discarded in the West End and are not recycled, ending up incinerated or in landfills.
Both papers have a circulation of more than 300,000 copies a day.
"We have the power in the Clean Neighbourhoods and Environment Act to ban the free distribution of literature in our area," said a council spokesman.
"We want to collect more for recycling, but the investment required for the extra recycling bins and collections is substantial.
"Due to limited space they would need to be a large number of smaller collection bins, which would need to be emptied at regular intervals throughout the evening."
The council said it has already set up bins to cope with the extra litter since the papers hit the streets last year.
A spokeswoman for News International said: "We have been working with Westminster Council since the launch of thelondonpaper and are now in further negotiations with them to resolve their current issues."
Associated Newspapers, publishers of London Lite, did not make any comment.