Midfielder Zheng, 29, is a free agent after being released by English club Charlton Athletic at the end of last season so the move would not governed by the transfer window, which closed on Tuesday.
Japan's Shunsuke Nakamura left Celtic for Spain's Espanyol in June and manager Tony Mowbray is hopeful of landing another East Asian playmaker in Zheng, who he also tried to sign at his former club West Bromwich Albion.
"Zheng Zhi is a player I have tracked for some time," Mowbray told Wednesday's Scotsman newspaper. "He is a highly-regarded player and was a thorn in our side when he played against us at West Bromwich Albion.
"I am delighted he may join us. He will significantly add to the squad with his quality and the fact he can play in a number of positions.
"We now need to tie up loose ends and obtain a work permit, which we hope to do before our next game."
Twice China's Player of the Year, Zheng joined Charlton, initially on loan, from Shandong Luneng when the London club were in the Premier League in late 2006. Versatility is Zheng's greatest attribute and he has played virtually every position on the pitch barring goalkeeper in his long international career.
Zheng would be the second Chinese player to play for the Glasgow club after defender Du Wei, who managed just 45 minutes of a Scottish Cup upset at Clyde in 2006 before heading back to Shanghai.
Celtic, who signed 20-year-old South Korea midfielder Ki from FC Seoul for an undisclosed fee last week, would offer Zheng a two-year contract, the Scotsman said.
