Hydrogen bonds are a type of intermolecular force that occur between a hydrogen atom covalently bonded to a highly electronegative atom (like oxygen, nitrogen, or fluorine) and an electron pair in a neighboring molecule.
Methane has only carbon and hydrogen atoms. Carbon is not electronegative enough to form a hydrogen bond, and the hydrogen atoms are bonded to carbon, not to a more electronegative atom.
Therefore, methane molecules only interact through weaker Van der Waals forces, not hydrogen bonds.