Virgin America (VA) shares closed up 3.6% Monday on expectations the U.S. Department of Justice was close to an agreement that will allow the company's purchase by Alaska Air (ALK) - Get Alaska Air Group, Inc. Report to win antitrust approval.

Virgin America rose to $55.55 from Friday's close of $53.60. Alaska Air's offer of $4 billion in cash is worth $57 per Virgin share.

A source familiar with the negotiations said in order to win DOJ approval the airlines have agreed to give up two to four gates in both the San Francisco and Los Angeles airports. Alaska will have to terminate its code-sharing agreement with Delta Airlines (DAL) - Get Delta Air Lines, Inc. Report and limit its code-sharing arrangement with American Airlines (AAL) - Get American Airlines Group, Inc. Report to markets where neither Virgin American nor Alaska have service. It was unclear whether the code-sharing with American will have to wound down completely over time.

Code shares enable airlines to sell tickets on one another's flights.

The Department of Justice declined to comment.

In April, the two carriers announced plans to merge. The DOJ in May extended its review of the deal beyond the obligatory 60 days, and in June, the airlines promised the Justice Department they would not close the deal until Sept. 30 unless the department concluded its review before then. On Sept. 26, the carriers agreed to extend that deadline to Oct. 17.

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After the Oct. 17 deadline came and went they had the option of closing the merger without approval but continued talking with the government on a settlement.

Alaska Air officials have said building business at California airports is the major motivation for the deal.

Alaska and Virgin each have six passenger gates at Los Angeles' LAX compared to the 10 gates controlled by Southwest. Alaska Air also shares three gates there with Delta.

At San Francisco International Airport the deal will make Alaska Air the second-largest carrier there, according to Chief Commercial Officer Andrew Harrison. After the acquisition it will have flights to all of the top 10 airports.

—Ted Reed contributed to this story.

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