He is said to have been interviewed for the post although he can be considered an outsider in a field which includes two lords, two knights - one of them a Tory MP - and the former boss of the hugely successful Royal Hong Kong Jockey Club.
Lindsay's own racing credentials are more modest. He has held bookmaking interests since 1975 - indeed, he has faced recurring criticism in rugby league over his reluctance to give up those interests - and has had a share in various horses.
In rugby league, he made his name as the vice-chairman and then chairman of Wigan, taking most of the credit for transforming them from comatose giants to the most successful club in the world.
He has found his four years in charge of the British game as a whole a more intractable proposition. Lindsay has courted controversy at home and abroad by brokering the pounds 87m deal with Rupert Murdoch that created Super League and summer rugby.
Lindsay has recently seen his power base compromised by the desire of the 12 Super League clubs for greater autonomy. They appointed their own chief executive, the former Daily Mirror managing editor, Colin Myler, at the end of last year.
In a brief statement yesterday he argued that being linked with the Tote chairmanship was a compliment to rugby league.Reuse content