Tony Blair has intervened in the hunting row by saying he would back a compromise allowing licensed fox hunts.
Hunt supporters are planning civil disobedience against a ban
Peers finished debating the Hunting Bill on Monday, backing licensed hunting and rejecting the total ban proposed by MPs for England and Wales.
The bill returns to the Commons on Tuesday and if there is no deal a ban could be forced into law this week.
No 10 says Mr Blair would back a plan to allow licensed fox hunts but ban stag hunts and hare coursing.
That idea was originally proposed by Rural Affairs Minister Alun Michael but MPs instead voted for a total ban.
On Monday, peers asked Environment Minister Lord Whitty whether the Parliament Act would be used to push the bill through if no deal was reached.
But there were Tory jeers as he replied: "I do not know."
He added: "It is not worth my time or the House's time speculating on what amendments if any will be put down to the bill tomorrow or what view the House of Commons will take of those amendments should they be so put."
Tory former minister Earl Ferrers said the use of the act would be "monstrous".
Mr Michael's proposals would allow fox hunts to continue if they met tests on cruelty and "utility" - whether they were needed for pest control.
Backing that package, the prime minister's official spokesman said: "The prime minister believes it is right to indicate the degree of his support for compromise."
It is unusual for Mr Blair to give such a strong signal about how he would vote.
BBC political correspondent Carole Walker said it was unclear whether he was prepared to stand up to anti-hunt MPs to try to get a compromise, or trying to distance himself from an outright ban which will provoke fury amongst hunt supporters.
Peers have so far voted for a licensing system, but they would allow stag hunting and hare coursing to continue.
The years of debate over a possible hunting ban could end with a "ping-pong" battle between the Lords and Commons this week.
The Parliament Act can be used to override peers' opposition if they try to thwart the will of MPs.
Commons Speaker Michael Martin is expected to say the conditions needed for the act to be used have been met, if there is no agreement before this session of Parliament ends on Thursday.
But the Parliament Act cannot be used to push through MPs' suggestion that a ban be delayed until July 2006 to allow time for hunts to adapt.
Some pro-hunt peers are proposing what is being dubbed the "kamikaze" option of rejecting any delay so a ban would be enacted within three months.
With hunt supporters planning a campaign of civil disobedience, they believe bringing in a ban quickly could embarrass the government before the general election.
Baroness Mallalieu, Labour peer and president of the pro-hunt Countryside Alliance president, said:
"There is a mood in the countryside that if we are going to be banned, get on
Lord Donoughue, a former Labour minister, said delaying any ban simply allowed the government "to wriggle out of facing the consequences of its policies during the election campaign".
But Douglas Batchelor, from the League Against Cruel Sports, said there could be no compromise and there was no reason to delay a ban.
He told BBC News: "What MPs have decided is that the ritual practice of chasing animals with dogs across the countryside and then killing them with dogs is cruel, is
unnecessary and should be banned.
"And I think that is what will happen this week."