Such a decision could clear the way for the election winner, former general Susilo Bambang Yudhoyono, to start speaking publicly about his plans and cabinet choices.
Susilo has so far held off declaring victory, waiting for Megawati to concede.
"The mood within the party is not to," said Roy Janis, deputy chairman of Megawati's Indonesia Democratic Party-Struggle (PDI-P) on Wednesday, when asked if a complaint over alleged vote fraud would be lodged by the Thursday deadline.
"I mean, Mrs Megawati has already said not to dwell on possible conflict and just move on. So among us, we have no intention of doing that."
Megawati's party had threatened to challenge the count from some areas, even though the independent election commission had declared the vote is valid.
It said Yudhoyono won by 25 million votes. Monitors had also said the ballot was largely fair.
On Tuesday, a tearful Megawati told Indonesians to accept the result from the 20 September run-off, but did not explicitly concede defeat to her former security chief.
Trying to make peace with his former boss and her powerful party, Susilo has refrained from celebrating, waiting for her to concede first. He quit her cabinet in March after a bitter row over his presidential ambitions.
Susilo has for now refrained from
celebrating and declaring victory
The election commission announced the results on Monday from Indonesia's first direct leadership ballot. That gave either side three days to complain to the constitutional court.
Aides to Susilo said he would make a political statement on Friday once the deadline had passed.
Susilo is scheduled to visit his mother in the town of Blitar in East Java province on Wednesday. He will also pay his respects at the grave of Megawati's father, Indonesia's first president and independence hero Sukarno.
Under the traditions of Indonesia's main island of Java, leaders are expected to pay homage to revered national heroes.