The answer is: No reaction occurs because magnesium (Mg) is less reactive than potassium (K).
Potassium is higher in activity series of metals and can not be reduced.
Metal X will replace another metal Y in a solution if X is higher in the activity series.
Activity series is an empirical progression of a series of metals, arranged by their reactivity from highest to lowest (alkaline metals have highest reactivity and Noble metals lowest reactivity).
Activity series is an empirical progression of a series of metals, arranged by their reactivity from highest to lowest (alkaline metals have highest reactivity and Noble metals lowest reactivity):
K > Ba > Sr > Na > Ca > Mg > Be > Al > Mn > Zn > Cr> Fe > Cd > Co > Ni > Sn > Pb > H(in acids) > Cu > Hg > Ag.
This series are used to summarize information about the reactions of metals with acids or water, double displacement reactions (more reactive metals displace metals with lower reactivity) and the extraction of metals from their ores.