Allardyce penned a two-year deal to become Avram Grant's successor on Wednesday, immediately setting his sights on leading the club straight back into the Premier League.
However, hamstrung by financial constraints, the club may begin life in the Championship without several key players. A summer clear-out appears inevitable, leaving Allardyce no option but to prepare for a host of players heading to the exit door.
Matthew Upson can leave on a free transfer while Ba and Cole are likely to favour a return to the top-flight - a scenario Allardyce has braced himself for.
"That's probably going to be the case for financial reasons," he said in the Daily Mirror.
On Parker's future, he said: "I don't know. It's difficult."