Alexander, who is tasked with turning around the ailing telecoms and broadband business, is also expected to announce several hundred UK job losses across Orange's 12,500-strong workforce.
The "future's bright" strapline, which has become one of advertising's most iconic lines, was coined in 1994 in Orange's launch ads created by WCRS.
Advertising breaking later this summer will no longer carry the slogan. The company's above-the-line advertising account is currently handled by Fallon.
According to reports, an email from the new boss was yesterday circulated to staff, which explained that he would be announcing plans to turn the business around. The email read: "There's a lot of change planned in order to put us back where we belong -- at the top of our game."
One area in need of a strategic rethink is Orange's broadband business, which has failed to make an impact in a fast-expanding broadband market, despite having established a foothold with its renamed Wanadoo service.
It lags behind rival broadband suppliers including BT, Virgin Media and TalkTalk. It lost around 35,000 broadband customers to competitors between September 2007 and March 2008.
Alexander is also expected to introduce measures to improve customer service, build on its 338-strong retail network and increase its network coverage.
The former Virgin Mobile boss joined Orange late last year, replacing Bernard Ghillebaert, who stood down from the chief executive role.