Eric Gao, chief executive of leading Chinese sports agency iRENA Group, told reporters on Tuesday that managers like the 68-year-old Briton were in demand in China.
"Lots of clubs want world-class football managers," he said. "But lots of football managers are not for sale here right now...I think he (Hodgson) has many chances.
"We'd love to sign him after this meeting," added Gao to some laughter.
Hodgson quit on Monday after England lost 2-1 to Iceland at Euro 2016 in one of the biggest shocks in English football history. One headline declared the loss to be "the ultimate humiliation".
Gao, who attended the match in Nice, said Hodgson would fit well with some of the Chinese Super League clubs he works with.
Former World Cup-winning Brazil coach Luis Felipe Scolari is at Guangzhou Evergrande while Sweden's Sven-Goran Eriksson, one of Hodgson's England predecessors, is at Shanghai SIPG.
Shanghai and other Super League sides are investing heavily in players and facilities as part of a soccer reform plan promoted by Chinese President Xi Jinping, an avid fan.
Xi wants China to one day host, and win, the World Cup and has set out a plan to create a sports industry worth $850 billion (638.28 billion pounds) by 2025.
Chinese clubs have gone on a spending spree to secure top Europe-based talent, and Gao expected more and more top players would be heading east.
The likes of Lionel Messi or Cristiano Ronaldo, he ventured, were probably out of reach even if Chinese clubs could outbid anyone else.
Gao expected to see increasing Chinese investment in European clubs but also money flowing the other way 'like an international marriage'.
"Lots of Chinese football clubs right now are wanting some international investors to be their shareholders as well," he said. "They want to change their DNA, not just keep the club by themselves.
"They want to invite some worldwide investors...to bring the coach, football manager, the players systematically not only one by one but group by group."
Chinese electronics retailer Suning Commerce Group's purchase of nearly 70 percent of Italian soccer club Inter Milan is the highest profile takeover so far of a European team by a Chinese firm.
Chinese investors have also bought into the Abu Dhabi-owned group that controls England's Manchester City.
(Editing by Clare Fallon)
