The presenter Gillian Marles, and Reevel Alderson, Kenneth Macdonald and David Allison, long-serving correspondents, have also accepted offers of voluntary redundancy, according to a report in The Times.
A former colleague told the paper: "The BBC is losing a bedrock of knowledge and experience in these people. They are fazed by nothing, [and] hugely admired by other broadcasters.
"This is a big loss.
"No doubt another generation is coming through but they have been standing on the shoulders of giants."
Eamonn O'Neill, associate professor of journalism at Edinburgh Napier University, said. "If this was an American network they would be throwing huge salaries around to keep these people,"
"Those networks hang on to their anchors, the people who have the best contact books in the business.
"If you look at Gordon, Izzy and Bill, that is a huge amount of credibility walking out of the door."
A BBC source, who asked not to be named, said it was "a challenging time for the BBC and Scottish journalism", adding: "There are talented younger people on the way up, but it will be important to retain a balance of experience in the newsroom, and make sure programmes have enough
staff to do the job."
A licence fee freeze meant the BBC had to find savings of £800 million over the first five years of its present charter period from 2017.
A further £125 million of cuts are being targeted after falls in licence fee collection and commercial income because of the pandemic.