The Manchester Evening News says Solskjaer was overheard uttering "Load of f****** nonsense" after a controversial VAR call went against United.
Friend initially issued Robert Brady with a yellow card, before heading to the monitor to give the challenge a second look.
There were fears in the Burnley camp that Friend could upgrade the booking to a red card, as Brady was the last man.
But instead Friend re-watched the build-up to the foul, and took a closer look at Luke Shaw's foul on Johann Gudmundsson.
He then decided that Shaw should have been booked for the challenge, so took play back to that moment, and retracted Brady's yellow card.