Speakman spoke to the supporter collective at a meeting that took place shortly before the end of the regular season, at which Neil's long-term future was discussed.
Neil has been said to be of potential interest to Burnley in the summer, and signed a 12-month rolling contract on Wearside when arriving in February.
Supporters asked whether Neil would have a say in recruitment, and whether the club would pursue a longer contract given the interest elsewhere.
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Concerns were raised that the head coach, who has overseen a 15-game unbeaten run en route to the play-off final, might not fit the club's model.
Speakman also told supporters that planning was under way for next season, with strategies in place whether or not Sunderland ultimately go on to win promotion from League One.
The minutes read: "Speakman confirmed there were [plans for League One & Championship football next season] and in many respects, they cross over as SAFC are in a unique position to compete for players who also have Championship interest. We will continue to seek improvement."
Part of the unease over Neil's future has been because he has consistently said that has not looked beyond the end of the season or discussed it with the club, though he has 'absolute clarity' on what he feels is needed to move forward.
In terms of the Sporting Director model, his comments when asked on Monday night about his pride in his team's achievements, given he did not sign any of them, suggests he is happy to work within the structure longer term.
"It's your job as a manager," he said.
"You see a lot of coaches going in to foreign teams where they don't sign players and all that sort of stuff.
"Providing you have an influence on what you want to do with the club and to take the club forward, that's the biggest thing for me. "I'm not power hungry by any means, but I have standards that need to be adhered to and if they are not, that's not going to be acceptable.
"Thankfully here, it's been 'here's your team, win games', and that's what I enjoy."
"KS believes it is difficult to dispel rumours that AN doesn’t fit as he quite clearly does and our recent record would suggest this," the minutes read.
"The intention of our working practices is to maximise skills and collaboration across the club for the benefit of the club.
"KS stated that club have a method of operating that’s been well documented in previous meetings.
"The player recruitment model is there to support the Head Coach, not to restrict him, and we also want our Head Coach to help evolve our working practices.
"We will never sign a player who the coach does not want."
Club figures also added that the rolling contract 'was common practice for most senior business positions', and that Neil had a similar contract at Preston North End.