The England international spent part of last season on loan at the Reebok and the Scot is reportedly interested in bringing him back.
Sturridge has been featuring for the Blues this season, however, and Villas-Boas insists that the 22-year-old won't be leaving Stamford Bridge.
"I know Owen very well and we spoke a lot early on in my career," he said. "I would say he is a good friend, and we have kept in touch since doing our Pro Licence together.
"We have exchanged ideas on players in the past, and he has put me under a lot of pressure about taking Daniel Sturridge on loan again, but I said absolutely not.
"He has left 20 to 30 messages with me about Daniel since I arrived here, and I expect more in January too, but he has no chance."
Since their opening day 4-0 win at QPR, Coyle's side have lost the following five league games and they currently sit bottom of the Premier League.
The Trotters take on Chelsea this Sunday afternoon at the Reebok.