Greenpeace activists GreenMyApple.org claim Apple may be preparing to take steps to address their criticisms of the company's environmental record.
The group has been vociferous in its criticism of the company, claiming Apple still uses hazardous substances in its products - substances other companies in the technology sector are abandoning.
Chemicals such as toxic flame retardants and polyvinyl chloride are used in Apple products. When these devices reach end of life they are disassembled, usually in developing countries. This process threatens the environment and the people who scour the dumping grounds, says Greenpeace.
Now the organisation is claiming that Apple chief executive Steve Jobs recently met with a Social Responsibility Fund investor, "to discuss Apple's environment record”.
While Apple has said nothing on this yet, Greenpeace claims Dutch Apple spokesperson Juriaan Bosman has said: "We are sticking to our strategy, but we don't rule out that at some moment our strategy will synchronise with what Greenpeace wants."
The activists are hoping Apple - which has former US vice president and environmental campaigner Al Gore on its board - will seize the chance to become the 'green leader' in the technology industry.
To achieve this, Greenpeace wants Apple to develop a better recycling programme and to use clean materials in its products.
A recent Greenpeace report showed Apple ranked lower than HP, Dell, Nokia, and Sony for its global policies and practice on eliminating harmful chemicals and on taking responsibility for products once they are discarded by consumers.