According to Swedish law, 90% of shareholders would need to accept the offer to enable Philip Morris to acquire the remainder.
However, PMI could choose to hold a majority stake in the company and keep it listed.
It could then look to mop up the remaining shares over time.
The Marlboro maker will decide in the next few weeks if it will change the deal conditions, the Bloomberg report said.
Philip Morris and Swedish Match declined to comment.
On Friday, activist investor Elliott Investment Management's stake in Swedish Match grossed 5%, making it the biggest shareholder in the tobacco and nicotine products maker.
Elliott has built a stake in the Stockholm-based firm in an attempt to oppose the nearly $16 billion buyout deal under its current terms.
In a filing to Sweden's financial watchdog Finansinspektionen on Friday, Elliott said it had increased its stake in Swedish Match to 5.25%.
The size of its previous holding was not disclosed.
Elliott declined to comment on the change in its holding.
On its website, Swedish Match lists Wellington Management as its biggest shareholder with a 5.1% stake, followed by Capital Group and BlackRock with 4.8% and 4.6% respectively.
Philip Morris last month extended the acceptance period of its May bid until 21 October from 30 September, and said it had so far received acceptances for around 0.24% of the shares.
Swedish Match stakeholders who have previously opposed the takeover include hedge fund Bronte Capital and investment firm abrdn.