Outgoing president Blatter confirmed on Monday a new man will be in charge of world football’s governing body by February 26 next year.
It is understood that Platini, currently UEFA president, has been urged by the majority of world football leaders to run for the top job.
And the Frenchman has the backing of Gill, the former Manchester Untied chief executive who worked alongside him on UEFA’s executive committee.
Gill said: “Any FA decision on the FIFA presidency will ultimately be a matter for discussion by the whole FA board. My own personal view is that Michel has done a first-class job at UEFA.
“I have seen what he has done for UEFA from the outside when I was at Manchester United and then having been on the executive committee of UEFA.
“He has not officially put his name forward yet, but he is a football man, he has the experience and, like any good leader, he has a lot of good people around him because you cannot do it alone.”
Gill also welcomed a series of proposed FIFA reforms including a limited number of terms for presidents and the disclosure of salaries.
He said: “There are a lot of good ideas and many of them echoes of what the FA has been proposing for some time. It’s important that the recommendations are taken to the congress in February to ensure FIFA does really start on a new beginning.”