Sources close to Wickremesinghe's United National Party (UNP) said they had received an invitation from Sirisena to meet later on Thursday evening.
It is unlikely that the trust vote - passed with the support of 117 MPs in the 225-member House - will help end the island's political impasse, especially coming a week after President Maithripala Sirisena declared that he would not appoint Mr. Wickremesinghe as Prime Minister, "even if all 225 legislators" back him.
A seven-judge bench unanimously ruled on Thursday that Sirisena can not sack the 225-member House before four-and-a-half years have passed since its election.
"As a country we have to be joyful that we have an independent judiciary that acted as a check on an errant executive", UNP deputy leader Sajith Premadasa said.
Sri Lanka is reeling from a constitutional crisis.
The parliamentarians of the UPFA were not present at the voting as they had boycotted today's (12) parliamentary session.
As many as 13 petitions have been filed against Sirisena's November 9 order sacking the 225-member Parliament, nearly 20 months before its term was to end.The Supreme Court on November 13 had issued an interim order ruling Sirisena's gazette notification as temporarily illegal and halted the preparations for snap polls.
"Moreover, it remains to be seen how Mahinda Rajapaksa will react", he said.
A spokesman for Sirisena did not respond to Reuters' requests for comment. He said the 19th amendment to the Constitution had made Sirisena powerless to remove a sitting prime minister.
Mr Sirisena had earlier said he would accept the Supreme Court's verdict, and some believe this could be the only logical way out of the quagmire that Sri Lanka now finds itself in.
Abraham Sumanthiran, a Tamil MP and one of the lawyers who argued before the court in favour of rejecting the president's order, said the court had reached a decision "that will no doubt go down in history as one of the most important".
In a widely-contested decision on October 26, Mr. Sirisena installed former President Mahinda Rajapaksa as Prime Minster, abruptly replacing Mr. Wickremesinghe.
But the judgment does not resolve the crisis, he said, as Sirisena has repeatedly refused to reappoint Wickremesinghe.
In a tweet, Mr Wickremesinghe called on President Sirisena to "promptly respect the judgment of the courts". Rajapaksa supporters had entered the same building in October in the aftermath of his appointment as prime minister and allegedly supervised the newspaper's coverage of the event.
But the attempted leadership switch has been repeatedly stymied by Sri Lanka's other branches of government. Lawmakers voted overwhelmingly on Wednesday to demand the reinstatement of Mr Wickremesinghe, but Mr Rajapakse has clung to the position despite not having the numbers in the Parliament.