Trade site MCV claims the two systems will be boxed together as an Ultimate Bundle, though specific prices and release dates were not discussed. The UK arm of PlayStation has previously hinted for and against the idea of selling such a hardware bundle.
In late September, Sony's Fergal Gara told CVG that "at the moment we're not thinking about a one-box solution. If we wanted to, it would be an easy thing to do, but we're not right now".
PS4 launched across North America on November 15 and has already amassed more than one million sales. The console launches on November 29 in Europe.
Vita launched late in 2011 and hasn't managed to catch the imagination of the games market. Global sales were hidden from the public when the system was still under three million units after a full year.
But in the UK, Sony is believed to have set aside some £2.5 million for Vita advertisements. The commercial messages are believed to connect the PS4 and its next major exclusive game, Tearaway.
Over a household's Wi-Fi box, Vita can stream gameplay from PS4, though is only feasible with a good internet signal and a relatively close distance between both systems and the Wi-Fi box.
"We're really excited for Vita as we move into Christmas," said senior product manager Ben Law.
"We've got a great campaign with key messaging around new releases like Tearaway, the ever-growing game catalogue and the Remote Play service."