As pointed out by WHO, the new coronavirus cannot be transmitted by mosquitoes.
Mosquitoes have the ability to transmit viruses, but they cannot spread all types of viruses!
Viruses transmitted by mosquitoes belong to the category of arboviruses (such as dengue, chikungunya, yellow fever, Zika, etc.), i.e. viruses that can replicate in the body of insects and overcome insect barriers and then be transmitted by bite. COVID-19 virus is not considered an arbovirus.
See also: The common European mosquitoes Culex pipiens and Aedes albopictus are unable to transmit SARS-CoV-2 after a natural-mimicking challenge with infected blood