Mr Mawhinney is from the Bellaghy area and left the family home at approximately 2pm on Saturday, August 8.
He was last seen in the Letterkenny area at around 11.40pm on Saturday night.
Inspector Gibson said: “Mr Mawhinney is described as being approximately 5’6” tall, of heavy build and has short dark brown hair.
“He is believed to be wearing a blue shirt, blue jeans, black jacket and black shoes.
“I would ask Declan, or anyone who knows of his whereabouts, to contact police on the non emergency number 101.”