The captain helped Palace to victory in the Community Shield on Sunday against Liverpool.
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With Guehi's deal now inside the final 12 months, Parish admits something has to give.
He said, "We'd have to do that, of course. For players of that calibre to leave on a free, it's a problem for us unfortunately.
"Joachim (Andersen) went (to Fulham last summer) and we couldn't afford to lose both.
"We then had another bid (for Guehi) in January but that was a different situation.
"We'll just have to see what happens. But, you know, it needs a new contract or a conclusion of some kind."