It is understood the library will find out in November if its bid has been successful.
The move is the latest setback to the troubled library. Before its opening it suffered cost and time delays, with building costs exceeding £500m – three times more than the original estimate.
John Ritblat, chairman and chief executive of property group British Land as well as being a British Library patron, has appointed engineer Buro Happold to confirm the status of the equipment and compile a report detailing the work that needs to be done.
The report, which has already been submitted to the government, will form part of a spending review that takes place every two years.
Should the government provide funding, the British Library will go out to tender for major capital works.