American lawyer Michael J Garcia refused to give details of what he would investigate, but said nothing was off limits.
That could also include investigating how much FIFA president Sepp Blatter knew about bribes paid to former FIFA officials from now-defunct marketing partners ISL.
A number of allegations of misconduct have been made about the 2018 and 2022 bids, including by former England 2018 bid chairman Lord Triesman.
Garcia told reporters: "There are no limitations at all on what we will be looking at. It will be determined solely by what we perceive as evidence or suggestions or reasons to look further and that will be our guiding principle - whether that is a particular World Cup or a particular person."
A Swiss court file said there was "no question" that Blatter and other FIFA executives knew about ISL payments to former FIFA president Joao Havelange and board member Ricardo Teixeira - leading to questions about why they took no action for more than a decade.
Garcia has launched one investigation into Mohamed Bin Hammam, who has been provisionally suspended for 90 days as a result, and he said he would also look into the ISL case.
Bin Hammam's lifetime ban for bribery was overturned in court last week, but since then an audit of Asian Football Confederation accounts has made fresh allegations against the 63-year-old, who withdrew from a challenge against Blatter for the presidency after being charged last year.