Foxconn, the Taiwanese company that assembles the bulk of the world’s iPhones, has offered about ¥625 billion ($5.3 billion) to take over troubled Japanese electronics makerSharp Corp., according to people familiar with the matter.

Sharp, which has been bailed out repeatedly by banks, is set to review a competing offer from Innovation Network Corp. of Japan, a government-backed investment fund. A person familiar with the matter said the fund was weighing a bid of around ¥300 billion, a figure earlier reported by the Nikkei...