Sources said ministers planned to lay the groundwork for a new Commons vote.
The government plans to set out its achievements in Iraq so far with RAF air strikes and training of Kurdish and Iraqi security forces, sources said.
The BBC also understands a small force could be sent to Libya.
The team of about 20 troops would be sent to help Libya secure its borders - which is seen as a crucial step towards stemming the flows of migrants into Europe.
An MoD spokesperson commented: "The UK, along with international partners, is supporting the process to form a recognised Libyan government and we are developing plans to provide support once this is done; it is too early to discuss the exact nature of this."
According to sources, ministers intend to argue that the mission to defeat IS now has to turn to Syria, and that the UK should play a role in that effort.
Describing the government's plans to increase its military involvement in the region, a source said: "The government is essentially posing a question: Could we do more? Should we do more? But Syria is where the fight should be taken to."
Another source added: "The government will say the campaign in Iraq has been a success. IS has been degraded, land has been taken back. Some of their leaders have been killed. But the problem is across the border in Syria."
Two years ago MPs rejected possible UK military action against Syrian President Bashar al-Assad's government.
A new parliamentary vote on the issue is not imminent, but the case will continue to be made throughout September in the run-up to the anniversary of the launch of UK airstrikes in Iraq, sources added.
They said any move to extend UK military action to Syria would only involve an extension of airstrikes against IS targets and involvement in coalition special forces operations.
The timing of the separate, small deployment to Libya is expected to depend on when Libya can form a unity government, and may be part of a broader effort. Nato is poised to go back into Libya to rebuild the country's defence and military once there is more political stability.
Nick Hopkins will have more on this story on Newsnight on Friday at 22:30 BST on BBC Two.

Bridgend county council wants to knock down Malc's Cafe in Rest Bay, to make way for the new modern facility.
Porthcawl Civic Trust Society has objected to the two-storey building saying it was "out of accord" with the area's character.
Councillors have backed it but said traffic plans must still be agreed.
The proposals were being considered by the council's development control committee on Thursday.
The council hopes the building - with public toilets, changing rooms, a new cafe/bistro, function room and covered dog walkers' area - will be used by water sports clubs.
Residents said the plans would increase parking problems, late-night noise and anti-social behaviour, and the height of the building would impact on the "unspoilt" appearance of the coastline.
The council said: "If successful, the water sports centre and cafe at Rest Bay will provide new high-quality facilities near the award-winning blue flag beach while establishing an iconic, contemporary attraction capable of supporting and developing sports and leisure activities in the area."
Approving the proposals, the committee has imposed a number of conditions in a bid to ease the public concerns.
The centre will not be allowed to operate after 21:00 in the evening and staff parking, turning area and delivery yard plans must be agreed.
The council said a traffic management plan for the development must also be submitted and approved before construction can get under way.

Solomona scored 40 tries in the 2016 season, including a record total of 40 in Super League.
Tigers chairman Steve Gill said in October that the 23-year-old Samoan was not for sale and would be returning to the club on 7 November.
BBC Sport understands Solomona has held talks with rugby union side Sale.
The Premiership club declined to comment on the story.
Ministers will start to make a case for British military action in Syria next week - with Downing Street keen to take the "next step" against so-called Islamic State - the BBC understands.
[NEXT_CONCEPT]
Plans to build a new water sports centre in Porthcawl have been approved, despite concerns it could spoil the coastline.
[NEXT_CONCEPT]
Castleford Tigers are to take legal action against winger Denny Solomona after he failed to return to the club for pre-season training.