Paul Levesque -- better known for his role as Triple H -- is a West Ham supporter and sent the 21-year-old a message about his future.
"Declan, you've got big decisions ahead of you and I understand that," he told BT Sport. "Far be it for me to tell you what to do but I'd like to give you a point of view that sometimes in life there are more important things.
"There's an opportunity to be something more. To be a hero, to be a hero to fans who supported you. To be a hero to people who have watched you come up through a system and be successful in that system.
"To be a hero and build something on your own. To not just succeed but to succeed on your terms. Build your franchise, build your legacy, to become something more.
"To become the one and only, to become the first. Declan Rice, build your legacy, build your franchise. Stay with the people that brought you to the dance.
"Stay with West Ham and become the hero, become the champion, become everything that they all know that Declan Rice can be."
Sources have told ESPN that the Hammers are determined to keep him but Chelsea boss Frank Lampard is keen on reverting Rice into the central defensive position he occupied earlier in his career, given his ability on the ball would enable him to play out from the back effectively.
The England international is contracted to West Ham until 2024 with an option for a further year.