Parkin, chief executive of the Clipper Group of haulage and warehousing companies, is preparing to step in with the help of new backers to help meet impending loan payments and avert another financial mess.
United, saved from administration last month by a consortium led by chairman Gerald Krasner, need to find £15m by July to repay a loan from property developer Jack Petchey.
Parkin, 43, is a long-standing member of Elland Road's Gold Club hospitality area and is believed to have been in talks with the board since last week.
According to Companies House documents, his firms made a pre-tax profit of £793,396 last year on turnover of £19.8m.
However, the offer has caused a boardroom split. Krasner and David Richmond support Parkin's involvement but fellow directors Melvyn Levy and Simon Morris are opposed.