Another option, Lucent said, is to form a joint venture for its Atlanta-based Optical Fiber Solutions business, a unit that makes optical fibers and related products.
The move comes after Lucent, based in Murray Hill, N.J., began a massive restructuring plan, hoping to reverse substantial losses and cut expenses by as much as $2 billion. The seven-point restructuring plan, outlined in January, includes laying off 10,000 workers.
Lucent's fiber business has about 6,300 employees and is in the midst of a $1 billion expansion program to try to meet demand.
The company said it is hoping to "better focus (its) resources and investments on the areas critical to (its) markets."
The French counterpart to Lucent, Alcatel, and manufacturing giant Tyco International are potential bidders for Optical Fiber Solutions, according to Reuters.
Lucent's troubles have been compounded by the market's continued decline, with the company forced to postpone initial public offerings of its spin-offs.
The company has twice changed the IPO terms of Agere Systems, an optical-components maker. If the Agere IPO actually takes place, it would be the second largest after AT&T's Wireless Group last year. There is some speculation that Lucent may sell Agere rather than take it to the capital market, Reuters previously reported.
Lucent stock has tumbled from a 52-week high of $75.37 per share and is hovering around $11 per share.