It said Slim had been in touch with Ronny Pecik - who with partner Naguib Sawiris has built a 20 percent stake in Telekom Austria - and Austrian state holding company OeIAG, Telekom Austria's biggest shareholder with a 28.4 percent stake.
The report - the second to mention Slim as a potential white-knight investor for Telekom Austria AG - could not be confirmed independently.
An America Movil spokeswoman in Mexico City declined to comment on the report.
With little left to shop for in Latin America, where it already operates in 16 countries, plus the United States, America Movil is turning its attention to Europe, where several telecoms hurt by the world economic crisis are emerging as buyout targets.
Last week, America Movil offered some $3.5 billion to boost its stake in Dutch telecoms company KPN NV to as much as 28 percent.
The company, which will formally submit the 8 euros-per-share bid to KPN shareholders in June, could pay for the KPN deal fully in cash and still have close to $1 billion left to make more acquisitions.
America Movil is a well-received commodity in the debt market, where its paper sells fast even in markets like China and Japan, suggesting it would have no problem in raising additional cash if the opportunity arises.
Tough conditions in Europe and fierce competition pushed core earnings at Telekom Austria down nearly 9 percent in the first quarter but the company stuck to its 2012 outlook.
The Austrian company faces a battle with Pecik and Sawiris who want seats on an expanded supervisory board at Telekom Austria.
Pecik has made his mark on other companies in which he built stakes with partners before selling again at a profit. Sawiris is one of Egypt's richest men who built a fortune in the mobile phone business and is now a liberal politician.
Both entrepreneurs may end up holding their stake in Telekom Austria for up to two years before selling to a strategic investor, Format reported, citing unidentified sources.
(Reporting by Michael Shields. Additional reporting by Cyntia Barrera; Editing by Erica Billingham and Carol Bishopric)