Warren Gatland has been offered the British
The BCC reported that the New Zealand-born Wales coach was interviewed for the position in London, following his side's Six Nations Grand Slam success and his appointment is expected to be finalised in the next month.
Should he get the job, he will be unable to coach Wales in next year's Six Nations, as the Lions want their coach to begin planning a year out from the tour.
Gatland, who was one of Ian McGeechan's many assistants in South Africa in 2009, would also become the second Kiwi to coach the famous composite side - after Graham Henry took the 2001 team to Australia.
The Lions will play a three-Test series against the Wallabies and several tour matches during their trek Down Under.
According to reports the Welsh Rugby Union, Gatland's full-time employers, had already paved the way for his Lions appointment by granting permission for him to miss the 2013 Six Nations.
According to the BBC WRU Chief Executive Roger Lewis has already spoken "informally" to Lions team manager Andy Irvine and Lions Chief Executive John Feehan about the prospect of Gatland coaching in Australia.
Gatland is expected to appoint his Wales defence coach Shaun Edwards to his backroom team, while England forwards coach Graham Rowntree, who was linked with a move to Wales in 2011, is also widely tipped to be one of his assistants.
The WRU are happy to ask Gatland's assistants Howley and Robin McBryde to lead Wales in the 2013 Six Nations and on their mid-year tour to Japan if Gatland was confirmed as Lions chief.
Gatland transformed Wales from 2007 World Cup flops to 2008 Grand Slam champions within months of taking the Welsh job.
He also guided Wales to an impressive fourth place at the 2011 World Cup before securing a second Six Nations clean sweep in 2012 - Wales' third Grand Slam in eight years.
Gatland also won the 2004 Heineken Cup and three English Premiership titles as Wasps coach.
B&I Lions 2013 schedule:
* Saturday, June 1 - Barbarians, Hong Kong
* Wednesday, June 5 - Western Force, Perth
* Saturday, June 8 - Reds, Brisbane
* Wednesday, June 12 - Combined NSW-Queensland Country, Newcastle
* Saturday, June 15 - Waratahs, Sydney
* Tuesday, June 18 - Brumbies, Canberra
* Saturday, June 22 - FIRST TEST, Brisbane
* Tuesday, June 25 - Rebels, Melbourne
* Saturday, June 29 - SECOND TEST, Melbourne
* Saturday, July 6 - THIRD TEST, Sydney
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