UPDATE 1-Mexico regulator yet to see Slim's telecom plan

* America Movil has not yet submitted plan to regulator

* Decision on plan could take three months (Adds detail, quotes, background, byline)

By Tomas Sarmiento and Noel Randewich

MEXICO CITY, Jan 22 (Reuters) - Mexico's antitrust regulator said on Friday that billionaire Carlos Slim has yet to submit his plan to combine his fixed-line and wireless telecommunications assets.

Slim launched a $21 billion plan last week to shift control of his Mexican fixed-line operator Telmex (TELMEXL.MX) and regional fixed-line operator Telmex Internacional (TELINTL.MX) into his flagship America Movil (AMXL.MX) cellphone company.

It could take up to three months to approve or reject the plan once it is submitted, Federal Competition Commission head Eduardo Perez Motta told Reuters.

"The (commission's) board will have to discuss ... whether to approve the operation without conditions, or to approve it with conditions, or not to approve it," Perez Motta said in an interview.

Slim's Telmex, which boasts around 80 percent of Mexico's fixed-line market, would be controlled by America Movil, which he also majority-owns, but the two companies would remain separate entities.

America Movil is a leading wireless operator in Latin America and has around 70 percent market share in Mexico, with Spain's Telefonica (TEF.MC) a distant No. 2.

Mexican regulators have tried for years to chip away at Slim's dominance of the telephone industry, sometimes fighting his companies in court. They have refused to let Telmex add television to its line-up of services, giving an edge to its smaller competitors.

"Sometimes his interests may coincide with the public interest, but sometimes not. And when they don't coincide, I think the public interest has to prevail," Perez Motta said.

Slim plans to tie up his companies by having America Movil acquire his holding company Carso Global Telecom (TELECOMA1.MX), which houses his controlling stakes in Telmex and Telmex Internacional.

Telmex Internacional, with fixed-line and Internet services in Brazil and other parts of South America, would eventually be delisted from the stock market and completely absorbed into America Movil, while Telmex would continue to be listed on the bourse.

Slim's plan to combine his companies follows in the steps of other sector giants, such as Telecom Italia SpA (TLIT.MI) and Deutsche Telekom AG (DTEGn.DE), to merge operations to keep up with fast-changing technologies. (Reporting by Noel Randewich and Tomas Sarmiento, editing by Gerald E. McCormick)