The discussions follow what is believed to have been a two-way pitch held by the Ontario Teachers’ Pension Plan (OTPP) earlier this year.
BPPA is understood to have competed against Westminster Advisers in the pitch.
The fund has invested in a range of infrastructure projects in the UK as a segment of its $117bn (£78.47bn) asset portfolio.
In 2010, it acquired 50 per cent of High Speed 1, the 109km rail line linking London with the Channel Tunnel, in a consortium with Borealis Infrastructure.
OTPP also owns sizeable stakes in Birmingham and Bristol International Airports, as well as 25 per cent of Scotia Gas Networks.
Last April, OTPP appointed BBPA’s sister agency Pelham Bell Pottinger to advise on its European and Asian corporate comms.
BPPA’s pitch is believed to have been led by Pelham Bell Pottinger’s new managing director Gavin Davis.
The potential appointment comes amid fresh calls to Chancellor George Osborne to increase spending on infrastructure as a way of dispelling Britain’s economic malaise.
Last week, Business Secretary Vince Cable suggested the Government could borrow more to fund capital spending.
Bell Pottinger Public Affairs and Westminster Advisers declined to comment.