The bill would create an independent regulator that could designate companies as dominant, impose stiffer penalties on them and even break them up to improve competition, said the draft obtained by Reuters.
The proposed reform would benefit Latin America's second biggest economy by lowering the prices consumers pay for telephone, internet and television services through greater competition, the government says.
Mexico's peso strengthened to its highest point in 18 months early on Monday with traders noting the currency had benefited from optimism on the country's reform drive.
The country's benchmark IPC stock index slipped 0.65 percent, dragged down by Slim's America Movil (>> America Movil SAB de CV) <AMX.N> and Televisa, which fell 1.84 percent and 1.65 percent respectively.
Televisa and a spokesman for Slim declined to comment on the reform, saying they did not have details of the plan.
The legislation, which President Enrique Pena Nieto is due to present at 1200 p.m. (06:00 p.m. British time), would also establish specialised competition courts to settle disputes, according to the draft copy.
Several proposals take aim at legal manoeuvres that Slim, the world's richest man, has used to skirt fines. The bill also contains requirements to allow competitors cheaper access to his vast network across the Mexican economy.
Slim controls about 70 percent of Mexico's mobile market and about 80 percent of fixed lines through his America Movil phone company. Televisa, controlled by media tycoon Emilio Azcarraga, has about 60 percent of the broadcast market.
Economists say the tycoons' control of their respective markets has subjected Mexicans to relatively high prices for services and dragged on the country's productivity as a whole.
The bill may face a tough road in the divided Congress, where no party holds a majority.
Opposition lawmakers have expressed concerns that the final draft may not be as radical as longtime advocates of reform have been demanding. If the bill is seen as soft, it could undermine a pact Pena Nieto made with the opposition to pass key energy and tax reforms this year.
"This seems too good to be true," said one lawmaker involved in the drafting of the bill and who requested anonymity due to the nature of the talks. "The devil will be in the details."
Under the draft bill, Slim's telecoms firms might be defined as dominant market players and be subject to so-called asymmetric regulations. That might, for example, allow smaller competitors to pay cheaper connection rates while making Slim's companies pay his rivals more to use their networks.
The agency "will impose limits on national and regional concentration of frequencies," the document said. The regulator "will order the divestiture of assets, rights or parts needed to assure the fulfilment of these limits."
Because details about the contents of the reform have still to be confirmed, stocks were suffering, analysts said.
"(Investors) are selling shares to eliminate risk, surprise," said Luis de Urquijo, strategist at compass Group in Mexico City. "I think the shares could recover a little if it turns out to be not as bad as it seems."
America Movil shares have fallen more than 11 percent since the start of the year, hurt by concern about the impact of the planned reform, as well as weak fourth-quarter results.
"If America Movil is forced to sell assets the value of the company will change and people prefer to be out of the stock while all this is decided," said de Urquijo.
Televisa shares are down 1.5 percent this year, after touching multiyear highs at the start of February.
Purely in terms of revenue, America Movil could be much harder hit by the reform than Televisa.
Slim's companies had 67 percent of the 414 billion pesos ($32.99 billion) in total revenue from Mexican phone and television companies in 2012, while Televisa's cable companies had just 8.5 percent, according to data from market research group The Competitive Intelligence Unit.
(Reporting by Michael O'Boyle and Dave Graham; Additional reporting by Elinor Comlay; Editing by Ron Popeski, Lisa Von Ahn and Andrew Hay)
By Michael O'Boyle