The offer is expected when Jean-Louis Beffa, the chairman and chief executive of Saint-Gobain, has a further face-to-face meeting with Sir Ian Gibson, the chairman of BPB.
The last time the pair met, two weeks ago, Beffa outlined a proposed offer for the company of 675p per share in cash, valuing BPB at £3.4bn.
BPB dismissed the offer as "substantially" undervaluing the company. BPB believes its business is in a strong position and that its shareholders would not be willing to settle for less than 800p per share, valuing the company at £4bn.
The BPB share price is currently 714p, but executives familiar with the situation believe that Saint-Gobain will have to offer at least 750p to be taken seriously.
Besides meeting BPB, Beffa will address analysts and institutional shareholders in London and present his case.
Beffa will tell analysts that BPB would be an ideal fit alongside SG Insulation, Saint-Gobain's interior insulation business. The two companies' products are often used together in building interiors and Beffa will stress the high growth, profitability and strong free cash flow that could be generated by combining them.
One executive close to the French company said yesterday: "Beffa is trying to show his shareholders that strategically buying BPB is a fantastic opportunity, that it is a great company and that its management is fantastic but that he is not going to overpay. He is trying to condition the UK market not to expect a big number."
BPB agrees that it is in a strong position with huge opportunities to take a bigger share of the plasterboard market, which is growing by more than 5 per cent per year.
Some analysts argue that BPB is worth around 740p per share or £3.7bn - equivalent to 8.7 times earnings before interest tax depreciation and amortisation. This is a similar valuation to that put on Aggregate Industries, the UK quarry products group, bought for £1.8bn by Holcim of Switzerland.
Saint-Gobain set to make fresh £4bn offer for BPB
BPB, the world's leading plasterboard business, is on full alert for an offer of more than £3.5bn for the company from Saint-Gobain, its French rival.