Sharp said it could not yet comment on the report except to say it was "considering various options for the restructuring of the LCD business". Hon Hai was not immediately available for comment.
Osaka-based Sharp was once a highly profitable manufacturer of premium TVs and a favoured screen supplier to Apple and others, but it has come under heavy pricing pressure from Asian rivals.
In May, it sought a bailout of roughly $1.9 billion from banks and promised to cut 5,000 jobs, or 10 percent of its staff.
Chief Executive Kozo Takahashi had initially resisted calls from investors for a more drastic overhaul of the LCD business, saying he was not considering a spin-off.
But in July, he told reporters that Sharp's losses, totaling 28.8 billion yen ($240.42 million) on an operating basis in April-June, meant it needed to consider more options.
Sources told Reuters last month that Sharp was considering a tie-up with Hon Hai as well as cash injections from other entities including the state-backed Innovation Network Corporation of Japan, a top shareholder in Sharp rival Japan Display.
Tie-up talks between Hon Hai and Sharp fell through in 2012 after the Japanese company baulked at demands that it said would have given the Taiwanese firm too much control. The two corporations remained in contact and jointly operate a plant in Osaka, western Japan, that makes large LCD panels.