The nomination of Liu, 63, who is also a board member of Foxconn's Japanese electronics unit Sharp Corp, would come after Gou, 68, said last week he would resign to demonstrate his determination to run in Taiwan's presidential election.
Foxconn-founder Gou told Reuters in April that he planned to step down as chairman of the world's largest contract manufacturer, so that younger talent could move up the ranks.
Liu's possible appointment came as a surprise for many at Foxconn due to his relatively junior rank among the Taiwanese firm's top executives, the people said on Monday.
The firm Gou founded, whose full name is Hon Hai Precision Industry Co Ltd, is trying to cut its dependence on Apple Inc and smartphone assembly by expanding into areas such as artificial intelligence and the internet of things.
Gou has repeatedly said that he wants someone "younger" to run Foxconn, one of the people said, adding that Liu has gained great trust since joining as a special assistant to Gou in 2007.
Liu has led Foxconn's nascent semiconductor business, dubbed the S sub-group, since 2017, the person added.
Through Liu, Gou would likely retain behind-the-scenes influence in strategic decisions, the person said. Such an appointment, however, is likely to have limited impact on day-to-day business because Foxconn's group companies have been operating independently for years, the person added.
Foxconn said in an emailed reply to Reuters that announcements of senior management appointments would be made according to the regulations of the Taiwan Stock Exchange.
"The operations of individual business groups remain unchanged and they will continue to operate under the leadership of their respective management teams," it said.
A stock exchange filing last week showed proposed candidates for a new board included Gou and Liu, as well as other executives widely linked to the group chairmanship such as Tai Jeng-wu, chairman at Sharp, and Lu Sung-Ching, chairman at Foxconn Interconnect Technology Ltd.
The board proposal is subject to approval at an annual shareholder meeting in June before a chairman can be elected.
Foxconn's share price fell 3% on Monday, while the benchmark share price index dropped by 1.4%. The stock is up about 17% this year, after falling 30% in 2018.
(Reporting by Yimou Lee and Taipei newsroom; Editing by Christopher Cushing and Alexander Smith)
By Yimou Lee