The Sky TV pundit has heavily criticised the attempt by United and English football's other Big Six clubs to launch a European Super League.
And there are concerns that Neville's continued attacks on the Glazers helped to fuel Sunday's violent protests at Old Trafford, with former Crystal Palace chairman Simon Jordan accusing the former United defender of "calling on a lynch mob".
While Solskjaer and his staff were against the ESL, they are upset over the postponement of the game against Liverpool and believe that Neville needs to tone down his rhetoric to avoid further unrest, says the Daily Mail.
The United boss made an unprompted reference to the issue on Wednesday, although the club's attempts to limit the number of questions about the protest prevented a follow-up.
"When it becomes a police matter that's not nice and it has not been helped by certain individuals," said Solskjaer.
"I have to say that's another part of it, that's your (the media's) end of it."