Ferguson launched a stinging attack on the organisation earlier in the week following their handling of the infamous "Boozegate" affair, which ended his Scotland career.
Former national team boss McLeish has confirmed he will speak to the player about the comments but hopes any dispute with the SFA is now over.
McLeish told BBC Sport: "I would rather it's swept under the carpet now. And I'd rather they just let sleeping dogs lie.
"Perhaps that will be his last comment about it, we'll certainly have a chat about it over a cup of tea."
Ferguson and his then Rangers team-mate Allan McGregor were told their international careers were over after indulging in a lengthy drinking session at the team hotel and then flicking V-signs at photographers while on the bench at Hampden.
McLeish added: "Barry's an individual and he's got freedom to a certain degree but he obviously feels aggrieved over the situation and maybe feels that he's been a scapegoat."