Emery worked with Jackson at Villarreal and is keen on a reunion.
The Mirror says any move for Jackson will hinge on Villa selling fellow centre-forward Ollie Watkins.
With Newcastle and Manchester United interested, Villa are now prepared to sell the England international.
Suitors have been quoted £60m for Watkins this summer, though that price could now drop with Emery pushing for Jackson's arrival.
Asked about his future, Jackson said last month: "I’m a Chelsea player. The future belongs to God. If there are any changes, you’ll know. For now, I’m focused on my preparation.’
"It’s football, there are ups and downs. Last season we won two trophies. There were difficult moments, moments of glory. Every season is like that. But the most important thing is to stay focused, to learn, and to grow in the face of adversity."