Vertex to Face ?

Yes, you can select the vertex and bevel it with control + B and then enter into vertex bevel with V.

Alternatively you can select the vertex and Shift + S to snap the cursor to selected and then Shift + A to add a circle and in the last operation panel that pops in the lower left, change the vertices to your desired mount.

In both cases you would need to add the supporting geometry to integrate the circle into the model. 

...Or SHIFT+CTRL+B to go directly into Vertex Bevel.

Problem here though, you can't make a circle from only 4 vertices.
However, you can bevel those new vertices again to create a circle.