Joint Opposition (JO) parliamentarian Ranjith Soysa said the motion of no confidence against the 68-year-old Wickremesinghe will be handed over to Speaker of parliament next week when the House resumes.
Rajapaksa told reporters yesterday that they were close to topple the government.
"He (Wickremesinghe) will have to go soon," Rajapaksa said.
The JO said the motion against Wickremesinghe will contain charges of economic mismanagement by him during the last 3 years.
It said that even some members of Wickremesinghe's United National Party (UNP) would sign the motion.
Among the top most charges against Wickremesinghe would be the alleged scandal in the Central Bank bond issues in 2015 and 2016, Sonysa said.
Wickremesinghe is accused of appointing Singapore national Arjuna Mahendran as the bank's governor whose son in law Arjun Aloysius was running a primary dealer firm.
He is also charged of failing to tackle the anti-Muslim riots in the central district of Kandy when he was the Law and Order Minister.
Since the February 10 landslide victory by Rajapaksa's new party Sri Lanka People's Party (SLPP), Wickremesinghe has faced calls for resignation.
The UNP, however, doubted Rajapaksa's ability to topple Wickremesinghe.
Both Rajapaksa loyalists and President Maithripala Sirisena's Sri Lanka Freedom Party (SLFP) are short of numbers to win the motion unless large scale defections from the UNP, which seems very unlikely.
The SLFP ministers who are in the Wickremesinghe's unity government cabinet said they will wait and watch.
They had called for Wickremesinghe's removal after the local election defeat to Rajapaksa but failed in their attempt to topple Wickremesinghe for the lack of numbers.
Sirisena replaced Wickremesinghe as the law and order minister on March 8 after fresh violence had erupted between majority Sinhala Buddhists and minority Muslims in the Kandy district, despite imposition of nationwide emergency.
Sinhalese Buddhists make up about 75 per cent of the population in Kandy.
Tensions between Muslim groups and the majority Sinhalese Buddhist community in the country have escalated since the end of the civil war in May 2009.
In 2014, violence directed against Muslim minority groups broke out in the southwestern town of Aluthgama, following a rally by hardline Buddhist nationalist monks, resulting in the death of at least three Muslims.