The tech giant's boss wants workers to return to the office at least three days a week by September but staff are demanding more flexibility.
An internal letter obtained by news site The Verge claims that the plans have "already forced" some Apple employees to leave the company.
The letter said: "Without the inclusivity that flexibility brings, many of us feel we have to choose between either a combination of our families, our wellbeing, and being empowered to do our best work, or being a part of Apple."
Management at Apple were also accused of a "disconnect" with employees over the issue of remote and flexible working.
It read: "Over the last year we often felt not just unheard, but at times actively ignored."
Employees have been working from home throughout the pandemic but Cook is keen to get back to an office environment.
A memo to staff said: "For all that we've been able to achieve while many of us have been separated, the truth is that there has been something essential missing from this past year: each other.
"Video conference calling has narrowed the distance between us, to be sure, but there are things it simply cannot replicate."
Cook also explained that he was missing the office environment.
He said: "I know I'm not alone in missing the hum of activity, the energy, creativity and collaboration of our in-person meetings and the sense of community we've all built."