Sanchez enters the final year of his contract this season and negotiations over an extension are yet to be concluded.
Some reports have suggested that the Chilean is holding out for wages between £300,000-a-week and £400,000-a-week.
"What I've heard that some of the reports that he wants serious money, you're talking £400,000-a-week at Arsenal which is unbelievable money," Parlour said on talkSPORT.
"Definitely a player you would miss if he does leave but somewhere you come to an end and you say we can't pay that money, it's just ridiculous to pay it.
"I said before, if it's in the regions of £300,000-a-week, I think I'd pay it.
"But when you get to £400-450,000-a-week, maybe if it is that sort of money they are talking about, then it's too much for me."