BERLIN — Shares of Nokia, the mobile phone market leader, climbed for a fourth day on Thursday amid speculation that the company may be poised to announce a software alliance with Microsoft designed to revive its struggling U.S. smartphone business.

Nokia’s shares have risen more than 4 percent since Monday when an analyst, Adnaan Ahmad of Berenberg Bank in Hamburg, urged the Nokia chief executive — and former Microsoft executive — Stephen Elop, to form an alliance that would put Microsoft’s Phone operating system on Nokia’s advanced smartphones.

Such a move would be a break for Nokia, which historically has avoided ceding key parts of its business, like software, to outsiders.

Mr. Ahmad’s letter to Mr. Elop, which was published in The Financial Times, advised Nokia to abandon its Symbian operating system for Microsoft’s Windows Phone software. With Symbian, Nokia’s share of the global smartphone market fell to 31 percent in the fourth quarter from 40 percent a year earlier, and its profit declined 21 percent.