The stock (TSX:PRQ) closed up about 2.3 per cent to $20.43 following various media reports out of Kuala Lumpur, which cited unidentified sources.
Industry Minister Christian Paradis rejected Petronas' offer on Oct. 19, but gave it 30 days to take another crack at winning approval.
A spokesman for Progress in Calgary declined to confirm whether its would-be acquirer had submitted a new application.
Both companies have met with Industry Canada to try to find out why the government rejected their deal — a move that dismayed many observers.
Petronas CEO Shamsul Azhar Abbas was quoted in the London-based Financial Times earlier this week as saying that his company would be prepared to add more independent directors to the Progress board.
He also told the Times that Petronas behaves like a publicly traded company and has worked to improve its governance and transparency in recent years.
Industry Canada, meanwhile, is weighing the larger and more controversial takeover of Calgary-based Nexen Inc. (TSX:NXY) by China National Offshore Oil Co. for $15.1 billion.
Nexen shares also rose Friday, about 1.7 per cent to $25.69.
That Investment Canada review, which has been extended twice so far, is set to end on Dec. 10. It can be extended in 30-day increments with the buyer's consent.
Prime Minister Stephen Harper said clarifications are coming soon to Ottawa's rules for takeovers by state-owned enterprises.