The 32-year-old, who is originally from Surrey, was last seen leaving an address in Basingstoke’s Popley area at 7.30 a.m. on Thursday, July 7.
Police and his family are deeply concerned about his well-being.
Extensive searches are being conducted to find him, and police are now appealing to the public for assistance.
Jack is described as white, about 6ft tall, and with black hair.
He was last seen dressed in a dark blue puffer jacket, dark blue jeans, and Vans sneakers.
He was also carrying a black bag, which was thought to be a bin liner. Hampshire police are urging anyone with information to contact them.
If you have seen Jack or have any information about his whereabouts, call 101 and quote 44220274226.