Hayek’s theoretical preference was to stabilize MV. This was not a policy suggestion. He wrote in Prices and Production,
Such a change in the “velocity of circulation” has rightly always been considered as equivalent to a change in the amount of money in circulation, and though, for reasons which it would go too far to explain here, I am not particularly enamoured of the concept of an average velocity of circulation it will serve as sufficient justification of the general statement that any change in the velocity of circulation would have to be compensated by a reciprocal change in the amount of money in circulation if money is to remain neutral toward prices. (1935, 123-124)
Don’t be fooled. A reading of the lines that follow this quote shows that he was not actually suggesting this as policy.
But quite apart from the particular difficulty which, from the point of view of pure theory, may not prove insuperable, it should be clear that only to satisfy the legitimate demand for money in this sense, and otherwise to leave the amount of the circulation unchanged, can never be a practical maxim of currency policy. (124)
In other words, Hayek did not approve of MV stabilization during the Great Depression. Nope. Instead, he waved his hands and said that policy probably will not accomplish what is theoretically possible. He then goes on to confuse the issue by considering changes in demand due to changes in production and trade. In this context he suggests that central banks should not expand the money stock "save an accute crisis", but apparently believed that even this sort of policy was to no good end no matter the reason. He explains,
In any case, it [expansion] could be attempted only by a central monetary authority for the whole world: action on the part of a single country would be doomed to disaster... The most we may hope for is that the growing information of the public may make it easier for central banks to follow a cautious policy during the upward swing of the cycle, and so to mitigate the following depression, and to resist the well-meaning but dangerous proposals to fight depression by "a little inflation". (125)
Hayek is unclear whether he is considering changes in y or V, not that it changes his conclusion. He clearly believes that central banks
cannot should not "fight depression by 'a little inflation'."