The 52-year-old host will be joined on the struggling ITV breakfast programme by Matt Barbet of Five News, according to The Sun.
The "top secret" proposal being offer to Kelly will reportedly see her come on air about an hour after Daybreak's current start time of 6am, and stay to front her regular show Lorraine immediately after.
"It doesn't take a genius to realise the answer to ITV's breakfast problems is staring them in the face," a source said.
"The audiences go up for Lorraine's slot and the reason for that is Lorraine. She is down to earth and someone British women can relate to.
"Everyone agrees this is something that could work. She was getting well over a million for her show even when [former Daybreak hosts] Christine Bleakley and Adrian Chiles were getting just a few hundred thousand for theirs."
The insider added that "no deal has been done" as of yet, while The Sun claims that Kate Garraway or Natasha Kaplinsky could still take on hosting duties.
Despite the shake-up, ITV producers are still believed to be axing Daybreak in the future.
The development comes as Kelly announced on Twitter that she has been discharged from hospital after undergoing surgery in the wake of a horse riding accident last week.
"Finally out of hospital," she wrote this morning (February 29). "Thanks for all your lovely tweets - really means a lot to know you are thinking of me. It was a bad accident but could have been so much worse.
She went on to praise the medical staff who treated her as "kind, caring and professional".