The former Anfield chief does not believe the Merseyside club would sell the Uruguay international to a top-four rival, but acknowledged the 26-year-old's desire to play in Europe
The Uruguayan has been the subject of two bids from the north Londoners, with the second, improved offer worth up to £42 million.
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"If the only offer is from Arsenal I would expect Luis Suarez to stay at Liverpool," Purslow told BBC Radio 5 live.
"It's disappointing as a follower of Liverpool that the player has so publicly and so early in the close season made it pretty clear that he would like to move on.
"I'm pretty realistic about these things and it's not that unusual for a player of that magnitude to want to play at Champions League level. That appears to be his motivation."
Like Purslow, ex-Liverpool director of football Damien Comolli believes Suarez is eager to showcase his ability in the Champions League, and the former Arsenal scout sees the Gunners as a step up.
"The longer Liverpool are out of the Champions League, the harder it will be to attract players. We knew it would be hard to keep [Pepe] Reina, [Daniel] Agger, Luis [Suarez]," Comolli told BBC Radio 5 live.
"Luis is extremely ambitious and with all due respect to Liverpool, they're a top eight side not top four like Arsenal".