Assertion:
Reversible process is quasi-static
Reason:
Quasi-static process is always reversible.
$\left( a \right)$ Both the assertion and reason are correct and reason is the correct explanation for assertion
$\left( b \right)$ Both assertion and reason are correct but reason is not the correct explanation for assertion
$\left( c \right)$ Assertion is correct but reason is incorrect.
$\left( d \right)$ Both assertion and reason are incorrect.

Hint: Quasi-static process: in thermodynamics this kind of process is also known as quasi-equilibrium because this kind of process happens slowly enough for the system to remain in internal equilibrium.
Example: quasi-static compression, where the volume of a system changes at a rate slow enough to allow the pressure to remain uniform and constant throughout the system.

Complete Step by step solution: Reversible process is the kind of process whose direction can be changed reversed to the initial or original state by inducing some changes to some property of the system’s surrounding. Although it would take a whole lot of time for the process to reverse hence the perfectly reversible process is impossible. Reversible processes change the system state in such a way that the overall change in the combined entropy of the system and its surroundings is zero.
A reversible process is a process which can reverse as explained above, and reverse the final state of the process to its initial or the original state, and by doing this, there would be no trace on the universe that the process ever occurred. Hence, we can consider reversible process as quasi-static
whereas, a quasi-static process is a kind of process which takes place very slowly, by doing so it is possible some time to be considered as a reversible process but not always in some cases only. Quasi-static process is not always reversible.
Therefore, the assertion is correct but reason is wrong.

Therefore, option $\left( c \right)$ is the correct option.

Note: We should know that the non-isothermal heat progression can certainly not be made reversible due to an inessential work term. We should also remember the basics of the all kind of process, as it will be helpful to solve similar such questions in future.