It is known to have been in talks with Vodafone since at least March this year, but the deal has so far failed to progress.
On Monday, Vodafone said that “the conditions to ensure thriving competition in the market need to be nurtured, otherwise the UK is at risk of losing the opportunity to be a 5G leader”.
At present, both Vodafone and Three UK lack the necessary scale to earn the cost of implementing this, Vodafone said.
“By combining our businesses, Vodafone UK and Three UK will gain the necessary scale to be able to accelerate the rollout of full 5G in the UK and expand broadband connectivity to rural communities and small businesses,” it added.
It said that the merged business would challenge the two already consolidated players for UK customers and bring benefits through adding another competitively priced 5G network.
According to Sky News, which first reported the latest round of talks, discussions between the two companies are now at a “relatively advanced” stage, though several significant hurdles remained outstanding, including whether the Competition and Markets Authority and Ofcom would allow the merger to go ahead.
There was no certainty that a deal would ultimately be reached, Vodafone said.
Previous reports have put the value of Three UK at around £6 billion.
On Monday morning, shares in Vodafone were trading at just over 100p, giving the company a market capitalisation of about £30bn.
Three UK declined to comment.