UN Security Council experts are discussing a strategy that would see the African Union force in Somalia extended from 12,000 to about 17,700 troops.
A spokesman for the UK mission to the UN said it wanted to "take advantage of what we see as a window of opportunity" to render al-Shabab militants "ineffective as a military force".
A draft resolution is expected to be circulated today, with a view to the resolution being adopted on Wednesday, a day before Britain stages a major conference aimed at breaking up the "business model" used by pirates in Somalia.
Senior representatives from more than 40 governments and international organisations will attend the London Somali Conference, starting on February 23 and hosted by the Foreign and Commonwealth Office, which aims to develop a new approach to tackle the threat of piracy.
Sir Mark Lyall Grant, the UK's ambassador to the UN, has said the purpose of the conference is to take advantage of the opportunity created by the military pressure on al-Shabab by a combination of the AU force, known as Amisom, and Kenyan forces.
Meanwhile, a new state-of-the-art global anti-piracy centre was unveiled today.
The intelligence hub has been set up by analysts Dryad Maritime in Portsmouth, Hampshire, to manage an international response to the threat of pirates which is costing shipping companies millions of pounds each year.
The centre is manned round-the-clock by a team of ex-Royal Navy warfare specialists and intelligence experts.
A Dryad Maritime spokeswoman explained: "Home to some impressive, state-of-the-art technology, the centre is pivotal in monitoring and analysing the movements, assaults and trends of pirate action groups around the world.
"To seafarers, the centre is a lifeline. It tells them where the pirates are, where they are headed and what they look like.
"When too close for comfort, the centre warns ships and they are diverted to safer waters."
Karen Jacques, chief operating officer at Dryad Maritime, said: "We expect the threat from piracy to continue, we are investing heavily in infrastructure and technology to give our clients an outsourced operations centre that rivals any naval force.
"Utilising analysis-led maritime intelligence can save on average three to four days for a vessel in transit with related savings to charterers and ship-owners on bunkers, hire and the employment of physical security teams amounting to around 90,000 US dollars to 220,000 US dollars per transit."
Dryad Maritime is a specialist maritime intelligence company employed by shipping firms to identify threats from piracy, terrorism and other criminal activity and to provide practical advice on how to avoid these.