The space around a charge is always under stress and experiences a force on another charge when placed there. The region or space in which stress exists is called the electric field (or dielectric or electrostatic) field. The stress in the space is represented by the lines of force. The electric field is a vector quantity.
The electric field is a force experienced by the charge divided by the magnitude of the charge and the magnitude of the charge is the modulus value of the charge. So if the charge is negative in nature, its magnitude will also be positive and therefore, an electric field can never be negative.
The electric field is a vector and thus has negative and positive directions. If an electron is negatively charged experiences a force against the direction of the field and if an electron is positively charged, it experiences a force along the field.
Hence, from the above point conclude that the electric field can be negative.