Senate Majority Leader Richard Saslaw said Friday that he is negotiating with Gov. Bob McDonnell and his staff to revamp the legislative redistricting plan to come up with a bill the governor might sign.

McDonnell (R) vetoed the original redistricting bill last Friday, accusing the Senate of sending him maps that split too many counties, cities and towns and one that did not receive any bipartisan support.

“We are talking to him,’’ Saslaw (D-Fairfax) said in an interview. “We are trying to meet all of his concerns.’’

Specifically, Saslaw said, the new plan would unsplit some localities.

An independent analysis of the boundaries released last week indicated that the districts in the original bill would have be less compact and divide more communities than the current districts. It found that the Senate would have divided 135 localities, compared with 110 under the current map.

Last week, Saslaw vowed that the Senate would simply adopt the same plan again and dared the governor to veto the map a second time.

But Saslaw said Friday that the Republicans in his chamber still may vote against the plan. Ten years ago, he said, the Senate plan did not receive any Democratic support in the Republican-led chamber and then-Gov. James S. Gilmore III still signed the bill. “I’m just not going to surrender my majority,’’ he said. (Sen. Benjamin Lambert (D-Richmond) did vote for the bill on final passage.)

The General Assembly returns Monday to resume work on the bill.

“I think it’d be great if the leadership could sit down at the table and say, ‘What do we need to do so that a majority approves it, to keep it from going to court,’ ’’ Sen. Ralph Northam (D-Norfolk) said. “The sooner we can all sit down and resolve this, and hopefully keep it out of court, the better off we’ll be.”

This post has been updated since it was first published.