The Tykes have held talks with Lee, who is also a majority shareholder at French side Nice, and his consortium, which includes US businessman Paul Conway, and hope for a swift conclusion.
Lee is looking for a full takeover but current owner Patrick Cryne could still retain a small percentage of the Championship club.
The Chinese billionaire made his fortune with hotel firm Plateno Group and the investment company NewCity Capital.
Sources close to Lee insisted that he is not planning to plough huge finances into Barnsley but is aiming to fund a push for Premier League promotion.
Barnsley had an impressive season last year, with manager Paul Heckingbottom steering them to a mid-table finish despite losing three key players , Sam Winnall, Conor Hourihane and James Bree, in January.
The consortium has previously seen an offer for Middlesbrough rejected by Steve Gibson and also spoke to Brentford earlier in the year about buying a stake at Griffin Park.