The 24-year-old is still recovering from a long-term hamstring injury. But even though he has not played for seven months, they remain keen.
Forest are ready to discuss a loan move for Chalobah.
However, because of the player's fitness record, the loan fee would be peanuts - around the £1 million mark.
Chalobah is close to a full recovery following his long lay-off.
If he can regain full fitness and play games then talks would be held over a permanent deal in the summer.
The transfer window shuts next Wednesday.
He is surplus to requirements under Blues boss Mauricio Pochettino and is keen on a fresh start.
Chelsea would also like to get his wages off the books as they plan for the future.
And, as an academy graduate, Chalobah represents pure profit in Financial Fair Play terms if he moves on.
Forest previously had Brazilian midfielder Andrey Santos on loan from Chelsea.
But the player was recalled after hardly figuring for the team, who sit just just four points above the drop zone.
