(UPDATE: The City Council voted 7-6 on Wednesday afternoon in favor of City Councillor Bill Linehan's plan. More here.)

A map redrawing the boundaries of City Council districts was expected to be finalized this week, as councillors were poised to vote Wednesday on a controversial measure that would shift 12 precincts in seven of the city’s nine districts.

District 2 Councillor Bill Linehan, who chairs the committee tasked with redrawing district boundaries, released a final report on Monday with the aim of gaining the approval of the full 13-member council on Aug. 22.

But the body faces the threat of a lawsuit if they approve the latest draft: “If Linehan’s map passes tomorrow, we will be suing," said Cheryl Clyburn Crawford, co-director of MassVOTE, one of several groups that comprise the Communities of Color Coalition.

Boston is required to redraw the city’s nine Council districts every 10 years, after the U.S. Census figures are released, in order to account for population shifts.

The figures have shown Boston’s population leapt 4.8 percent to 617,594 people. But the shift left some districts imbalanced, including Dorchester’s District 3. That forces the council’s redistricting committee to add residents to some districts and move residents out of over-populated districts, like District 2, which includes South Boston.

Councillors have been split over how to solve the problem – often compared to a Rubik’s Cube – particularly if it meant dividing neighborhoods. The possibility of two councillors moving or giving up their seats was raised in the early stages of the process.

Local redistricting activists have called for a total overhaul of the council districts, demanding more opportunities for candidates of color and decrying a set-up that has remained unchanged since the 1980s. But, their proposed map did not appear to gain traction inside City Hall.

Linehan’s map includes the following proposed changes:

--District 3, represented by freshman Councillor Frank Baker, picks up the Polish Triangle (Ward 7’s Precincts 8 and 9) and loses two Lower Mills precincts (Ward 17’s Precincts 12 and 14). District 3 also gains Ward 7 Precinct 7, which includes Carson Beach, and Ward 7 Precinct 10 and Ward 13 Precinct 5.

--District 4, represented by Councillor Charles Yancey, picks up two Lower Mills precincts that Baker loses, as well as Ward 13 Precinct 4.

--The South End remains split between several Council districts, with two precincts moving into District 7, represented by Tito Jackson. District 2 adds the City Hall precinct (Ward 3 Precinct 6) while dropping the Dorchester precincts (the Polish Triangle).

--Only Districts 5 (Roslindale, Hyde Park and Mattapan) and 9 (Allston/Brighton) escaped without any changes.

“This Committee has embarked on fulfilling the goals of legal compliance, creating or preserving neighborhood unity where possible, accounting for the demographic shifts, and limiting disruption for voters,” Linehan wrote in the committee report. “The Committee fulfilled its commitment to a public process by conducting redistricting hearings throughout the neighborhoods of the City of Boston, taking testimony from an array of interested persons, and conducting several public meetings in City Hall. The attached plan embodies the fulfillment of the Committee’s redistricting goals, public comment, and Councillor concerns.’”

Councillors must send an ordinance detailing the changes to Mayor Thomas Menino’s desk in the next few months, since any person running for City Council in the 2013 elections must be living in their respective district 12 months before the election.

But the coalition’s lawsuit may throw a wrench into the timetable.

The coalition includes NAACP-Boston, Chinese Progressive Association, ¿Oíste?, the Lawyers Committee for Civil Rights and Economic Justice and Project HIP-HOP.

"We’re very disappointed that we weren’t able to negotiate something, that we have to go this route," said Crawford on Tuesday afternoon.

Voting rights activists won a similar lawsuit about ten years ago after State House lawmakers redrew legislative district boundaries. Activists claimed the boundaries diluted minority voting strength and protected incumbents. The lawsuit led to House Speaker Thomas Finneran's resignation and subsequent indictment. Finneran eventually pleaded guilty to obstruction of justice and he was disbarred by the state's highest court.

The coalition alleges that the Linehan map violates the Voting Rights Act of 1965 and "packs" District 4 with 95 percent people of color, diluting the potential impact of minority votes elsewhere in the city, like Dorchester's District 3. The groups had proposed splitting District 3 and 4 horizontally, with District 3 in the north and District 4 in the south, instead of the east-west split currently in place.

Linehan did not immediately respond to a request for comment.

District 3’s Baker said he is still deciding which way to vote on Wednesday. “I’m still thinking about it. We’ll see what happens on the floor," he said. "There may be amendments."