Does there exist any relation between metallic property and oxidation potential?
The short answer is yes. The reason for this is that metals exhibit metallic properties because their electrons are relatively loosely bound to the atoms. A metallic bond is one in which the valence electrons are free to move throughout the lattice structure of the metal. Here's a schematic diagram from wiki commons:



The idea is that the positively charged metallic "cores" (which includes the nucleus and the more tightly bound inner core electrons) are sort of suspended in a crystalline structure within a "sea" of mobile electrons.

This model explains most of the  metallic properties we observe, from heat and electrical conductance, to malleability and ductility.

Now think about oxidation - in an oxidation-reduction (redox) reaction, one element gains electrons (it is reduced) and the other loses electrons (it is oxidized). Here's an animation, also from wikipedia:



So, for an element to be metallic, its valence electrons need to be relatively "loose" - it can't take too much energy to detach them. For an element to be oxidized, something else has to "want" the electrons more - the energy cost of removing the electron has to be lower then the gain from adding them to the reducing agent.

As a result there is a very strong correlation between the metallic nature of elements and their relative ease of oxidation. There is also a very strong correlation between both of these properties and the trends in ionization energy, electron affinity, and  electronegativity.

Of course, in chemistry, things are never that simple. There lots of details and it is tough to make general statements that are always true. For example, you can say that often times the more "metallic" an element is, the more easily it will be oxidized. However, when you compare elements using a standard electrode potential table (which gives us a way of measuring relative ease of oxidation) you find that it is easier to oxidize calcium ($-3.8 \space \rm{V}$) than it is to oxidize potassium ($-2.9 \space \rm{V}$), even though potassium is closer to the "metallic side" of the periodic table, it has a lower first ionization energy, and it is less electronegative.

This illustrates a limitation of thinking of elements in terms of metals and non-metals: it is really a shorthand way of describing all of the things that affect how tightly those valence electrons are bound to the atom, in comparison to how badly other elements "want" to remove them. With that amount of generalization, we lose too much detail to be able to make accurate predictions in every situation.