After selling its handset division to Microsoft, Nokia may be considering a buying Alcatel-Lucent's wireless business. 

According to a Reuters report citing people familiar with the matter, talks between the two companies were described as "on again, off again," with the most recent discussion held in late 2012. 

Nokia could not be reached on the matter prior to press time. A spokesman for Alacatel-Lucent declined to comment on the matter, saying the company's "priority is to execute The Shift Plan in order to give us the means to manage our own destiny."

A tie-up between Nokia and Alcatel-Lucent would give both companies a leg up in the battle against large equipment vendors Ericsson, as well as Chinese companies like Huawei and ZTE. 

The reports come after shares of Nokia soared following the news earlier this month that Microsoft had officially agreed to acquire Nokia Corporation's devices and services business for a total transaction price of $7.2 billion in cash. 

Reuters points out that analysts are pegging the value of Alcatel's wireless business at between $1.49 billion to $2.03 billion.

Shares of Alcatel were up nearly 3 percent Thursday at the opening bell to $3.68, while Nokia down slight at $6.61.