Such a move could potentially lead to the closure of its 164 department stores and put 11,000 jobs at risk.
BHS used to be owned by retail tycoon Sir Philip Green and formed part of his Arcadia group, which includes other well-known high street names such as Topshop, until the department store chain was sold for £1 to Retail Acquisitions last year.
The company has piled up a mountain of debt of more than £1bn, and has a pensions deficit of £571m.
Last month, the retailer reached an agreement with landlords for a Company Voluntary Arrangement (CVA) which would result in their bill for rent on the majority of its stores being reduced.
Malcolm Weir, head of restructuring and insolvency at the Pension Protection Fund, said: "We have been in talks with BHS to find a solution for the pension schemes following the CVA last month. Members of the BHS pension schemes can be assured they are protected."
Reports that BHS could be about to file for administration first surfaced on Friday, and a source close to the CVA told City A.M. that it was expecting to raise additional finance but nothing had been announced as yet.
"Raising finance has been a sticking point," he said.
Meanwhile, the BBC also reported that Sports Direct has been keen to buy BHS, but is put off by the prospect of having the plug the gap in the pension fund.
Trade union Usdaw, which represents a number of shopworkers, has said in a statement that it is "very concerned" about the speculation of the possible administration.
"We are seeking urgent clarification from the company and urging them to change their attitude to trade unions and begin a dialogue with us at this difficult and worrying time for staff," said David Gill, Usdaw national officer. "We also urge the company to comply with the law, consult staff and Usdaw as the union for BHS workers on the future of the business."
Neither BHS nor Sports Direct has responded to City A.M.'s request for comment as yet.
Last month, it was revealed that the company was planning to slash around 150 jobs at its head office in a bid to keep the company afloat, and a spokesperson said that several vacant positions had also ben closed as part of cost-cutting measures.