According to the Mail Online, Donald was abused by Black Cats supporters after their 2-0 loss at Fratton Park.
Christian Burgess and James Bolton were on target as Kenny Jackett’s side leapfrogged their fellow League One heavyweights into the play-off places.
The Stadium of Light chief was reportedly leaving the ground with his son when travelling Sunderland fans targeted him, causing Blues supporters to step and defuse the fracas.
Donald, who purchased Sunderland in May 2018 after selling non-league Eastleigh, has come under pressure as the Wearside outfit aim to escape the third tier at the second time of asking.
The club has been up for sale publicly since December.