The cigarette price war reportedly could send the industry's Nos. 1 and 2 U.S. players into each other's arms.

R.J. Reynolds

( RJR) and

British American Tobacco's

TST Recommends

( BAT) have recently discussed a merging their domestic tobacco operations, although the talks have been sporadic and a deal isn't imminent,

The Wall Street Journal

reported Wednesday.

The companies face pressure from the onslaught of discount cigarettes lately flooding the market, as well as a cutthroat discounting campaign from

Altria's

(MO) - Get Report

Philip Morris.

The issue of which company does the acquiring has sunk similar talks in the past. In the transaction currently under consideration, R.J. Reynolds would acquire Brown & Williamson, but the situation is fluid and could change, the newspaper said.

Among the obstacles any deal would face are antitrust rules that would probably require Brown & Williamson to sell off a number of brands, and a possibly exorbitant capital gains tax if BAT were to sell Brown & Williamson.

R.J. Reynolds closed Tuesday at $38.13, up 48 cents, or 1.3%. BAT closed at $21.74, down 37 cents, or 1.7%.