Investors from the group are said to have been shown around the ground and are considering an offer to buy the League One-bound club.
The Sun report Shandong Luneng tried to buy the club last year, but talks with owner Ken Anderson stalled.
In recent trips to England, they have been accompanied by ex-Bolton sports scientist Mark Taylor, who worked with Allardyce at Wanderers, Blackburn, Newcastle and Sunderland.
Allardyce is remembered fondly by Bolton fans after guiding the club into the Premier League in 2001 and reaching the last-32 of the UEFA Cup, now known as the Europa League, five years later.
He managed the club between 1999 and 2007 before leaving for Newcastle.
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Shandong Luneng have a club playing in the Chinese Super League, but reportedly want to own an English team.
Despite living locally, the former England boss could be put off by a return as Bolton are set to start next season on -12 points after Anderson and a company acting on behalf of late owner Eddie Davies’s Trust put the club into administration.
On Wednesday, Anderson said there was ‘little or no choice’ but for ‘one of us’ to take action, however a club statement said papers have been filed by both parties.