Deal nears in United board fight: Sources

United Airlines activist on the record
United Airlines activist on the record

A deal between United Continental and two hedge funds seeking to shake up its board looks increasingly likely, sources told CNBC on Monday.

An agreement may come within the next week, the sources added.

The hedge funds, Altimeter Capital Management and PAR Capital Management, collectively hold a 7.1 percent stake in United. They announced last month that they would nominate six directors to United's board amid concerns about its stock performance.

Oscar Munoz, CEO of United Airlines.
Source: United Airlines

The proxy fight has escalated, and United pilots even protested the funds in Boston last week. Altimeter and PAR have said they are not targeting CEO Oscar Munoz, who recently returned from medical leave, but United's board.

United's agreement with the funds could include new directors in addition to the three independent directors added last month, sources said. An agreement could also bring an independent chairman, they said.

United declined to comment.

Altimeter and PAR could not immediately be reached for comment.

Activist: New board would help United CEO succeed

CNBC's Scott Wapner contributed reporting.