The two companies will hold board meetings on Wednesday to approve the deal and officially sign a deal the following day, said the two sources with direct knowledge of the talks.
Both of the sources declined to be identified as they are not authorised to speak to the media.
A Sharp spokesman declined to comment, while Foxconn officials were not immediately available for comment.
Foxconn, formally known as Hon Hai Precision Industry Co, is set to cut its earlier JPY 489 billion ($4.3 billion) offer for newly issued Sharp shares by about JPY 100 billion, the sources said.
The companies had come close to signing a deal last month but Foxconn hit the pause button following revelations of previously undisclosed liabilities at the Japanese company.
The deal would be the largest acquisition by a foreign company in Japan's insular technology sector. In choosing to negotiate with Foxconn, Sharp turned down a rival offer by a state-backed fund.
It would also boost Foxconn's position as Apple's main contract manufacturer and provide Sharp with funds to start mass-producing organic light-emitting diode (OLED) screens by 2018, around the time Apple is expected to adopt the next-generation displays for its iPhones.
© Thomson Reuters 2016