Rivals such as AT&T and Telefonica have been anxiously awaiting new rates since the Supreme Court ruled in August that America Movil should not be barred by law from charging other carriers for calls to its customers.
The court found the market regulator, the Federal Institute of Telecommunications (IFT), not legislators, should set the so-called interconnection rates.
The decision weakened a key pillar of a 2014 reform intended to loosen Slim's grip on a market he has dominated since taking control of former state phone monopoly Telmex in the 1990s.
A proposal drafted by the IFT's regulatory policy unit would allow America Movil to charge 0.03686 pesos per minute for mobile calls made to customers on its network next year, and its competitors to charge 0.1176 pesos, the document showed.
The seven IFT commissioners are set to vote on the proposal on Friday, according to three people with knowledge of the matter. However, they cautioned the schedule could change.
The unit of regulatory policy could revise the draft before the vote, and the rates ultimately approved by the commissioners could differ from the proposal, they said.
A spokesman for the IFT said no plenary session had been scheduled for Friday so far.
A spokeswoman for America Movil declined to comment.
Currently, in line with the 2014 telecoms reform that was one of President Enrique Pena Nieto's signature accomplishments, America Movil cannot charge other carriers for calls made to customers on its network, even though those firms can bill Slim's firm for using theirs.
Competitors had urged the regulator to keep the zero interconnection rate, or something close to it. Broadcaster Grupo Televisa, for example, recommended America Movil should be permitted to charge no more than 0.015 pesos per minute.
Created by Slim in 2000, America Movil later swallowed its parent Telmex, and by the end of last year, it held about two-thirds of Mexico's mobile subscriptions, according to IFT data.
The zero rate had been a particularly effective part of the reform, said Alexander Elbittar, a researcher with Mexico's CIDE university. To further strengthen competition, the gap between America Movil and its rivals in interconnection rates should remain as wide as possible, he added.
"As long as you keep reducing the spread, you are going to be hurting the business for the minor operators," Elbittar said.
If the rates proposed in the document are approved, the gap would be cut to some 0.08 pesos from about 0.19 pesos this year. Still, experts say the IFT must balance promoting competition with encouraging investment in Mexico.
Speaking at an event in the central city of San Luis Potosi on Monday, Slim criticized Telefonica and AT&T for not investing enough in the telecoms infrastructure. AT&T entered Mexico after the reform, spending $4.4 billion to buy two carriers.
Before legislators agreed on the zero rate in 2014, the regulator had allowed America Movil to charge 0.2 pesos per minute, compared to 0.3 pesos for competitors.
If the IFT allows Slim to charge again, it could alarm rivals. After the Supreme Court ruled against the zero rate, Telefonica, which has long struggled to grow its business in Mexico, said it had been gravely hurt by the decision.
The ban on charging rivals for network usage has been one of the main drags on America Movil's profits in the reform.
Slim topped the Forbes global rich list for four years until 2014 as the reform started to bite.
(Reporting by Julia Love and Christine Murray, additional reporting by Noe Torres; Editing by Dave Graham and Himani Sarkar)
By Julia Love and Christine Murray