The Sunday Times, quoting analysts, said that Slim could be planning to use his IN&M stake as a bargaining chip in a potential deal in the Caribbean mobile phone market, where O'Brien has interests through his company, Digicel.
Slim owns America Movil, Latin America's dominant mobile company, which has been mooted as a potential buyer for Digicel. However, O'Brien has said his company is not for sale.
Analysts said Slim could use his IN&M stake to undermine O'Brien's ambitions to acquire IN&M.
O'Brien has been building up his stake in the group since late 2006 and now holds a 21% share. He has been labelled as a "dissident shareholder" by the IN&M board for his frequent negative comments about the company's strategy and O'Reilly.
O'Reilly, whose family controls 28% of INM, has vowed to resist O'Brien's calls to sell off The Independent and The Independent on Sunday.