The no confidence motion would be non-binding – a type of debate that allows members to express their opinions on a topic but does not force action.
Carroll says the motion is currently being considered by the Stormont Business Office.
It needs the signatures of at least 30 assembly members to force a debate.
Sinn Féin has 27 elected representatives in Stormont.
On Saturday, its assembly member Deirdre Hargey confirmed the party will support the PBP motion.
She said Givan’s actions had undermined public confidence in his ability to serve in office.
“The education minister’s decision to travel to Israel and use departmental resources to promote that trip is both inappropriate and unacceptable,” she said.
Hargey also attended Saturday’s rally and said Sinn Féin “will look at all options to hold the education minister to account”.
It appears Carroll will secure the support he needs as the Social Democratic and Labour Party (SDLP), which has eight assembly members, also said it backs the motion.
The party said it is “willing to use our Opposition Day time on Monday 10 November to ensure it is debated as soon as possible”.