David Cameron has "sympathy" with calls for the rules on foxhunting to be loosened, Downing Street has said.
MPs and campaigners are pushing the Government to scrap the ban on using more than two dogs to flush out foxes so they can be shot.
Farmers say attacks on lambs have increased, and argue that limited pest control measures permitted under the 2004 Hunting Act are not working.
They point out that the change - likely to require a vote in Parliament but not a fresh Bill - would bring the law in England and Wales into line with that in Scotland.
Any move to ease the restrictions on hunting introduced by the Labour government would be highly controversial, but potentially popular in Tory heartlands.
Derek Morgan, chairman of the Farmers' Union of Wales's hill farming committee, told the Daily Telegraph: "The hunting ban was aimed at what Labour saw as posh people on horses.
"But the people who have suffered most are working-class hill farmers. If Government increased the number of hounds we are allowed to use, it would reduce the number of lambs we lose."
The Prime Minister's spokesman said: "There is a very specific issue here around pest control and the impact it has on particular farming communities, such as hill farmers.
"The Prime Minister has some sympathy with these concerns. They have been voiced by MPs from across the House."
The spokesman said the coalition agreement included provision for a free vote on hunting, and declined to rule out holding one before the general election.
"Given the cross-party nature of concerns raised in this area, is is something the House may wish to consider," he said.
"There are various ways in which the House can consider these things. I wouldn't guide you in any particular direction.
"We are at the stage where concerns have been raised. The House in various guises may be looking at this further. We will have to wait and see what further views there may be."