UK prime ministers do not legally need to consult Parliament before launching military action, although they have done so since the 2003 invasion of Iraq.
Mrs May is due to give a Commons statement on Monday before facing questions from MPs.
She is also expected to ask the Speaker for permission to hold an emergency debate in Parliament on the issue of Syria.
Any vote would be "largely symbolic" and would mainly just acknowledge that Parliament has had its say rather than give MPs the chance to formally approve or reject the air strikes themselves.
Theresa May's decision to authorise action without MPs' backing has been criticised by Labour leader Jeremy Corbyn, who said she could "easily" have recalled Parliament or delayed her decision until MPs returned to Westminster from the Easter recess.
Mr Corbyn called for a new War Powers Act "so governments do get held accountable to Parliament for what they do in our name".