The Wigan-based Tote, which was set up in 1928, comprises 540 high street betting shops and 59 betting shops on race courses, as well as the pool betting system.
The consortium that has been invited to bid includes the Race Course Association, the Racehorse Owners Association and the Racecourse Holdings Trust.
The government said it had requested a bid be made by January 26.
The move would knock other bidders, including Europe's biggest gambling firm, Gala Coral, which had already offered é405m, as well as a consortium with backing from South Africa's Phumelela and Australia's Tabcorp. The government pledged in 2000 to sell the Tote to the racing industry, but an attempt last year to sell it was blocked by the European Commission, which said the price was so low it constituted state aid.
Following the Commission ruling, the government had the Tote valued by accountancy giant Pricewater houseCoopers - at a reported price of about é400m - and invited offers. An initial bid of around é320m from the racing industry consortium was rejected.
Some racing industry players have questioned whether the Tote will be able to meet its mandate of investing in racing, if its new owner is burdened by heavy interest payments after funding the deal with debt.
A government statement was silent on how a deal might be funded, but said: "The new proposal meets the government's commitment to ensure racing benefits from the sale."
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