Dear Friend,
The answer is the Management can extend the age of retirement to 60 years. There are no legal restrictions to do so. However before effecting that, you in HR must do some home work.
1) Is this request coming because getting replacement is difficult?
2) Is it because of trade union demand? or if union exists then you may have to sound this change to union.
3) is the employee concern in good health to carry out duty for the forthcoming years
4) once the policy is changed for 60 years retirement, it will become a precedent and you will find it difficult to change it later.
5) Are you going to give this facility to select few by discretion or to all and who will apply discretion from Management side?
6) whether top management supports this move?
7) what increments or benefits will be offered to the employee for the extended period?
You can formulate a HR policy based on responses to the above and if satisfied, may implement.