The Asian Football Confederation president is a leading candidate to succeed Sepp Blatter but remains under scrutiny over his role in Bahrain's Arab Spring uprising in 2011.
Last week another candidate, Prince Ali of Jordan, publicly questioned whether Sheikh Salman protected Bahrain players who alleged abuses after pro-democracy protests.
Sheikh Salman, a member of Bahrain's royal family, has strongly and repeatedly denied wrongdoing.
But English Football Association chairman Greg Dyke told the BBC today: "Can you have someone from Bahrain running world football, in charge of world football, given what happened there four years ago? I personally have my doubts."