Multiple sources with direct knowledge tell TMZ ... Britney wants to hire powerful lawyer and former federal prosecutor Mathew Rosengart. Britney has signed the following document:

"Pursuant to my statement in open court on June 23, 2021, my rights, and my desire to end the above-referenced conservatorship as to my father Jamie P. Spears, it is my desire to choose and retain my own counsel, at Greenberg, Traurig, LLP as set forth above."

The document is signed "BRITNEY JEAN SPEARS"

Rosengart, a partner in the firm, has represented a number of high-profile clients over the years, including Steven Spielberg, Sean Penn, Ben and Casey Affleck, Eddie Vedder, Soledad O'Brien, Michael Mann and NBA star Jimmy Butler.

TMZ broke the story ... Britney's long-time, court-appointed lawyer in her conservatorship case, Sam Ingham, resigned earlier this week. Our sources say Ingham believed he could no longer represent Britney because, in part, of her comments in court that she was never informed until recently she could end the conservatorship. We're told Ingham and others dispute that and say Britney was told numerous times over the years -- many times on the record in court -- that she could end the conservatorship, but she always declined to do so.

Britney became increasingly upset over the years ... especially with her dad, and wanted him out both as the conservator of her person and conservator of her estate. Jamie resigned as conservator of her person but remains sole conservator of her estate.

Bessemer Trust was scheduled to become co-conservator of Britney's estate but withdrew a week ago.

Our sources say Rosengart and his team have not formally agreed to represent Britney, but if he does the mission will be to attempt to end the conservatorship, although the first step is removing Jamie.

Britney has already asked the judge to end the conservatorship without any further medical evaluation. That will be an uphill climb, because nearly 2 dozen doctors and therapists have weighed in over the years ... saying Britney has a serious mental illness that would imperil her safety if left to her own devices. The judge did not indicate whether she's receptive to bypassing a mental health exam as a pre-condition to ending the conservatorship.

The other hurdle Britney must jump -- she's in a conservatorship, so she's unable to enter into a contract without the approval of her conservator. The person who must sign off -- none other than Jamie Spears. This would explain why the first step would be to attempt to remove Jamie.