Sunderland were relegated from the Premier League in the 2016-17 season and immediately dropped to the third tier before being taken over by a consortium led by Donald in May 2018.
However, following a goalless draw against Bolton Wanderers last month, supporter groups of the ninth-placed side issued a joint statement calling for the club to be sold immediately following a poor run of results.
"Co-ordinated, 'no turning back' campaigns... against owners are highly unusual at any club particularly after 18 months," Sunderland said in a statement.
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"Given these circumstances, and Donald's sincere commitment on his arrival at Sunderland that 'I won't outstay my welcome', the board feels that it has no option but to sell the club.
"That process has now commenced. Owing to confidentiality agreements, there will be no further updates until a preferred bidder is identified."
Donald, who met with Sunderland supporters in December and promised to invest in players in January, thanked fans and urged them to continue backing the team and manager Phil Parkinson.
"We would also like to reassure those loyal fans that we are placing sufficient funds in the club to support the manager as he seeks to improve the first team in the next few weeks," Donald said.
Sunderland were beaten 2-1 by Charlton Athletic in the League One playoff final last season but have lost six and drawn eight of their 23 games in this campaign.
"Whilst progress on the pitch has been slower than all associated with Sunderland would have liked, the club has become one of the very few in the EFL to be debt free and break even on an operational basis," the club statement added.
"With that stable base... and with the team now back in contention for promotion, the board believes that Sunderland continues to head in the right direction."
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