text: The news comes as MPs prepare to debate stripping him of his knighthood.
  One MP voiced scepticism to the BBC about the timing, arguing it made the issue "essentially cash for honours".
  BHS, sold by Sir Philip last year, subsequently collapsed with 11,000 jobs lost and a £571m pension deficit.
  Sir Philip has vowed several times to sort out the pension problem, telling MPs in June that his advisers were working on a "resolvable and sortable" solution.
  On Monday, he told ITV that he was in a "very strong dialogue" with the pensions regulator to find a solution, but would not put a number on the level of financial support he would be willing to give.
  A damning MPs' report on the High Street chain's failure, published in July, concluded Sir Philip had extracted large sums and left the business on "life support".
  At the time Sir Philip described the report as "the pre-determined and inaccurate output of a biased and unfair process".
  A debate in the House of Commons on Thursday will discuss whether Sir Philip's knighthood, awarded in 2006 for services to retail, should be removed.
  Should they vote on the issue, any such vote would not be binding.
  The issue would be for the Honours Forfeiture Committee - part of the Cabinet Office - to decide.
  Sir Philip's knighthood hinges on whether he makes good on a promise to secure the future of 20,000 BHS pension scheme members.
  As things stand, many of them face a cut in their pension benefits if the scheme ends up in the industry backed pension protection fund.
  Despite repeated assurances, so far he has tabled no firm offer.
  But, the BBC has leaned that a meeting with the pensions regulator to work through obstacles to a final deal is scheduled before the end of the week.
  The decision on whether to have a vote on Thursday on his knighthood rests with the speaker of the House of Commons. It falls to him to decide whether it is worth waiting to see if Sir Philip can produce a deal before MPs vote on whether to start the process of removing his title.
  MPs contacted by the BBC have expressed scepticism about this latest offer - one described it as essentially "cash for honours".
  BHS pension scheme members will care more about their retirement income than this game of parliamentary poker.
  Read more from Simon
target: Former BHS owner Sir Philip Green will meet the pensions regulator by the end of the week to try to secure a deal over the collapsed retailer's pension fund, the BBC has learned.