The Mirror says the Moroccan football agent could not resist dabbling in team affairs.
Lemsagam oversees Oldham's signings and had a big say in team selection and tactics under Scholes' predecessor, caretaker boss Peter Wild.
This was unacceptable for Scholes, who knew such interference completely undermined his position as manager, and he quit on Thursday afternoon after just 31 days and seven games in charge.
Scholes said in a statement: “It is with great regret that I have decided to leave the club with immediate effect.
“I hoped to at the very least, see out my initial term of 18 months as the manager of a club I've supported all my life.
“The fans, players, my friends and family all knew how proud and excited I was to take this role.
“In the short period since I took on the role it unfortunately became clear that I would not be able to operate as I intended and was led to believe prior to taking on the role."