Parish spoke about several other Palace players, including Fulham’s second offer for Guehi’s central defensive partner Joachim Andersen, believed to be £25m plus £5m in add-ons.
Palace rejected Fulham’s first bid of £20m on Monday, and value the Denmark international at closer to £40m.
“That’s an interesting one because I can’t imagine a situation where we would lose both of our centre-halves,” Parish said.
“Again, Joachim, he’s a special lad and very much at the heart of what we do. He’s like our quarterback at the heart of that back three, a sensational footballer.
“We have got to sit and think about what is the right thing to do, what the players want to do. If both of them are still here at the end of the window I wouldn’t be surprised.”
The Eagles have already sold star player Michael Olise to Bayern Munich for £50m and are braced for interest in England international Eberechi Eze.
Eze was of interest to champions Manchester City last season but they signed Matheus Nunes instead. Parish says there has not been any “concrete interest” in the forward this transfer window.
“Everyone is in a trading deficit in the Premier League. If you want constancy, you have to first of all attract the right talent and part of that is showing them a pathway,” he said.
“Players like Michael [Olise] going to Bayern and going to the top clubs in the world shows people that coming to Crystal Palace you can get picked for your country, you can go and play at the highest level.
“What do we hope? One day we are the Champions League club that everybody wants to come to, we’re the Europa League club that everybody wants to come to.
“Up until then we have to be realistic. We have to work with the players, work with the sporting department, we have to make sure we have a good squad and we are making smart decisions about recruitment – buying and selling.”