Ms Lumley said she was very hopeful agreement could be reached
Joanna Lumley has said she trusts Gordon Brown to do the "right thing" for the Gurkhas after meeting with the prime minister to discuss the issue.
Ms Lumley said Mr Brown had taken the matter "into his own hands" and would come up with a "solution" to the issue of residency rights by the end of May.
The actress has long campaigned for all Gurkhas and their families to be given the right to settle in the UK.
No 10 said the prime minister was considering Ms Lumley's arguments.
The Lib Dems said the government must "act quickly" to give the Gurkhas what they wanted, saying the UK had a "simple moral obligation" towards them.
And Keith Vaz, the Labour MP who chairs the Home Affairs Committee, has written to Mr Brown asking him to clarify whether the government's position has changed following the meeting with Ms Lumley.
The prime minister suffered a shock Commons defeat on the issue last week, forcing ministers to reconsider existing rules on how many Gurkhas can settle in the UK.
Some 36,000 Gurkhas, a brigade of Nepalese soldiers who serve in the British Army, were denied UK residency because they left before 1997.
Ms Lumley described her meeting with Mr Brown as "extremely positive" and said the prime minister was "wholly supportive" of the Gurkha cause.
Ms Lumley said she wanted Gurkhas to be given the same rights to settle as soldiers from Commonwealth countries who had fought for the UK.
She said Gordon Brown was a "man of integrity" and she was "absolutely confident" that an agreement could be struck now that he was intervening personally over the issue.
"I trust him," she said of the PM. "I rely on him and know he has now taken this matter into his own hands."
She said Mr Brown would bring forward proposals for reform of the existing residency regulations by the end of the month but could not disclose details on what these changes may be.
No 10 said the meeting, which took place in Parliament and was not attended by any officials, was "friendly and constructive".
But it said it still planned to complete its review of the regulations by the end of July, not - as suggested by Ms Lumley - by the end of this month.
Ministers were forced to review the rules after losing a vote in Parliament, which saw 28 Labour MPs vote against the government and more than 70 others abstain.
The government has said it would process all current applications by Gurkhas for residency by the end of May and review the criteria for residency before MPs' summer recess.
The BBC News Channel's chief political correspondent James Landale said there still seemed to be a difference of opinion between the two sides over the timing of the review.
But he said Downing Street sources were indicating that the review of existing applications, due by the end of May, would set a "precedent" for the outcome of the wider look at the rules.
Earlier Mr Brown told MPs the government would "listen to the voice of the House" in re-examining the existing regulations
Mr Brown has argued that, under the current system, about 10,000 Gurkhas and their families will be entitled to settle.
He said he wants to do more for the Gurkhas but that any further promises must be affordable and not undermine the government's wider immigration policies.
The government has said an "open door" policy for admitting Gurkhas could cost up to £1.6bn but opposition parties and some Labour MPs have questioned these figures.
Opposition parties are pressing the government to come up with concrete proposals to allow all Gurkhas to settle in the UK, no matter when they served in the army, as soon as possible.
Lib Dem leader Nick Clegg said any further delays or unfulfilled promises towards the Gurkhas would be "downright cruel".
He told Channel 4 News that many Gurkhas were old and frail and "could not wait much longer for Gordon Brown to do the decent thing".
And former Home Secretary David Blunkett said most people wanted all Gurkhas to be given the right to live in the UK but this must be done "gradually and sensibly".
Ms Lumley's meeting with the PM was hastily arranged on Wednesday after she told MPs she had written three letters to Mr Brown about the issue which went unacknowledged - a point No 10 disputed.