The former chief executive of the tour company Thomas Cook - who has been described as "greedy" and "shameless" - will reportedly donate to charity a third of the shares she is entitled to.
This follows widespread criticism of how Thomas Cook has treated the parents of Bobby and Christi Shepherd who were found dead in a bungalow in the grounds of a hotel in Corfu in 2006 having died from carbon monoxide poisoning.
Harriet Green, the company's former chief executive, will donate a third of her shares to charity, according to ITV News.
It is believed that Ms Green could receive six million shares next month and the programme says she will reportedly give two million shares to a charity to be chosen by the children's parents.
ITV News said it is estimated that the shares could be worth £2.9 million.
Earlier this week it was reported that Ms Green was likely to receive a £10.5 million bonus from the firm later this year.
She led Thomas Cook until last year during a period in which the firm took legal action against the hotel involved and fought to stop inquests into the children's deaths taking place in the UK.
The conclusion of those inquests earlier this month provoked a new wave of criticism of the holiday giant after the jury decided Christi and Bobby were unlawfully killed and said the tour company had breached its duty of care.
Since then, it has been revealed that the firm secured a £3 million compensation payout from the company that owns the hotel.
Ms Green's payout was criticised by former Downing Street adviser Steve Hilton who told BBC One's Andrew Marr programme on Sunday that she was a ''greedy shameless boss''.
The children's mother, Sharon Wood, told The Mail On Sunday: ''Harriet Green has behaved shamefully towards us - she refused to meet us. She should hand this bonus back, or pay it to children's charities.''
Ms Green's spokesman said earlier this week she ''has enormous sympathy with the family'' and that ''she has watched the events of recent weeks with some distress and is personally disappointed with the company's handling of the inquest''.
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