Mr Manele's coalition fell apart a week ago when 12 ministers quit, leaving him without a parliamentary majority.
Rather than test his numbers in parliament, the prime minister appointed new ministers - among them four-time prime minister Manasseh Sogavare as his deputy - and continued on.
There are fears that the political impasse could also produce public disorder.
Local outlet In Depth Solomons reports that an opposition MP's home was attacked on the weekend, which the opposition has blamed on supporters of the government.
The opposition force includes ex-prime minister Darcy Gordon Lilo, Opposition Leader Matthew Wale and Peter Shanel Agovaka, who walked out as Mr Manele's foreign minister last week.
They claim the support of 28 MPs in the 50-seat parliament, and have called Mr Manele's decision not to recall parliament "intolerable and unacceptable".
"From past experience, the current political crisis, if not resolved quickly, has the potential to have very serious social and economic effects, including a constitutional crisis," they wrote in a letter to Mr Manele, as reported by In Depth Solomons.
Mr Manele dismissed those concerns at a press conference on Sunday.
"All ministries are fully covered. Cabinet remains functional and continues to meet and take decisions necessary for the effective administration of government," he said.
It's the third time Mr Manele has faced a serious political crisis in his two years as prime minister, with the Isabel-based leader surviving previous pushes.
One previous notice of no confidence failed to materialise, and last year, he defeated a second motion by recruiting opposition MPs.
This time around, the 28-strong grouping appears firm - as evidenced by a number of group photos they have distributed.
The Island Sun reports that Mr Manele's political situation is made worse by two government MPs with serious medical conditions, meaning they would only be able to summon 20 votes.
Should the no-confidence vote pass, the opposition will likely be invited to form a government without elections, or it could dissolve parliament and send the 850,0000-strong country to the polls.
The Melanesian nation is no stranger to political instability.
Major unrest meant Australian and New Zealand peacekeepers and police were stationed in the country for more than a decade to 2017.
In 2021, riots again broke out following the country's decision to recognise Beijing rather than Taiwan, producing three deaths, scores of arrests and millions worth of damage.
The Solomon Star also reports that 600 workers at Honiara's port are set to go on strike on Tuesday, which could inflame the situation further.
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