No. Heat transfer in solids is always by conduction because molecules of the solids remain relatively at fixed places.
Convection heat transfer occurs when there is a bulk fluid motion.
If the fluid(liquids and gases) is stagnant (not moving) it transfers heat only through the conduction mode of heat transfer. So, it can be said that the conduction heat transfer by the fluid is a limiting case of convection heat transfer wherein the fluid does not move. An example of this is a gas trapped between two glasses of double-glazed windows. The air does not move and it can only transfer heat through the mode of conduction.