Lai's firm Yunyi Guokai Shanghai Sports Development only took over the Midlands side on September 15 of last year but have already been approached about selling the club on, according to business network Bloomberg.
The offer is thought to have been for £180m, only slightly more than the reported figure of £175m when Lai purchased the side last year, and is well short of the club's current estimated value of £200m.
West Brom chairman John Williams confirmed: "My information is that there was an enquiry. Our majority shareholder made it clear that he wanted to retain control of the club and continue his plans for its ongoing development."
All four of the West Midlands' leading sides are now under Chinese control, with Wolverhampton Wanderers, Birmingham City and Aston Villa also having gained new owners in the last 15 months.