Chelsea should wrap up a £7million deal for the England international in the first week of January, says the Bolton News.
"It would be a massive blow to lose Gary," he said. "He is a great player and a great asset for the club. Unfortunately, his contract is running out. Whatever happens, happens, but hopefully it's the best for him.
"Wheater played well before he was suspended and we have to believe we have got good enough players to turn this thing around.
"I personally think the squad is strong enough as long as we stop those mistakes we have been making at the moment."