It was reported over the weekend that Green, who has been working with Magic Circle outfit Linklaters and Big Four firm Deloitte to design a deal with the Pensions Regulator, could be writing a cheque for around £300m to plug the collapsed retailer's pension scheme. Those close to the negotiations say they are progressing well.
Former pensions minister Ros Altmann said such a move "would be welcome as long as it meant the members get more money and that the scheme doesn't have to go into the Pension Protection Fund (PPF)".
Altmann added she hoped the situation could be dealt with as quickly as possible so "workers know where they stand and so that this whole scandal can go away".
Craig Mackinlay, MP for South Thanet and member of the Work and Pensions committee, called the news "a very welcome step in the right direction," adding "[Green's] doing the right thing".
Tom McPhail, head of retirement policy at Hargreaves Lansdown, said: "Since he appeared in front of the select committees back in June, there's been almost complete radio silence from Sir Philip Green. People were starting to wonder whether he was actually going to make good on his promise to do right by the scheme members."
However, McPhail warned the recent news did not mean the BHS saga was done and dusted, and more pension-related announcements were likely in the pipeline. "Everything is really focused around what more could be achieved for the scheme members to take them somewhere closer to the 100 per cent benefits they were originally promised," he said.
The 88-year-old BHS was put into administration back in April, placing 11,000 jobs on the line and raising questions about the pensions blackhole worth £571m.
Administrator Duff & Phelps announced in June the business would need to be wound down, as no suitable buyer could be found, and the final 22 stores shut their doors for good on Sunday.
BHS' collapse also sparked two parliamentary inquiries and the final MPs' report branded Green's behaviour as "the unacceptable face of capitalism".