David Moyes has given a more positive update on his future as Sunderland manager after productive talks with Ellis Short, the club's owner, and Martin Bain, the chief executive, this week.
Allardyce said: "If we are safe and Jermain Defoe is available, and he wants to come to Crystal Palace, I would be interested".
He also spoke of his sympathy for David Moyes' plight at Sunderland.
"We've got our fingers in the pie on quite a few players and we'll see how we go on those players".
"I know what needs to be done to get back in the Premier League and I know what the requirements are to do that", he added. "I came to a part of the country I was led to believe that's how they wanted to be spoken to and I told them exactly".
Sunderland may only have pride to play for now but can still have a big say in the relegation battle with games against fourth-from-bottom Hull City on Saturday night (EST) and Swansea City (currently in the last relegations spot) next week. We were deflated, I wouldn't say it was an uplifting kind of meeting. "I've got a four-year contract so I don't know what you're talking about "a decision".
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"I'll tell you if the agent is telling the truth or not".
Sunderland have been actively looking for new investment and the club's latest accounts revealed they have debts of more than £110m.
He said: 'When I look back on it I was very honest, forthright, told people what I thought.
The future is less certain for England global Defoe, who has a clause in his contract that allows him to leave the club as a free agent in the event of relegation.
The Scot also said striker Jermain Defoe, who has scored 14 goals this season, could leave the club. What that is isn't yet clear, but anything less than £20 million will be met with derision by Sunderland fans.