The 127-member body meets on Thursday to hear a presentation from FA executives about why they are backing the stadium's sale to Fulham owner Shahid Khan.
According to 'BBC Sport', the board is slightly against the sale overall, as some councillors believe that the home of English football should not be sold to a foreign backer.
The council includes representatives from the Premier League, Football League and county FAs and is often referred to as the parliament of English football.
They have no power to formally veto the sale, but the FA board has made it clear that their approval is essential for allowing the deal to go ahead.
If approved, the FA board would then meet at a yet to be decided date to rubber stamp the deal.