The 28-year-old has struggled for playing time at Stamford Bridge, but Allardyce believes that Chelsea boss Jose Mourinho will be unwilling to let him go.
"I'm not so sure you'll be able to get Demba Ba with Romelu Lukaku on loan at Everton," talkSPORT quotes Allardyce as saying. "Jose will want three strikers.
"We have stated that we want to strengthen a certain area. That will get hundreds of agents picking the phone up to tell us who they have available. The phone is starting to get warmer. It's not red hot yet."