Suarez has fallen out with the Anfield hierarchy after claiming that Liverpool manager Brendan Rodgers had "promised" to help him leave if the club failed to qualify for this season's Champions League.
Rodgers has flatly denied Suarez's claims and promised to discipline his star striker whilst club owner John W Henry has insisted the Uruguayan will not be sold at any price.
Arsenal have already had two bids for Suarez rejected by Liverpool - the latter of £40m plus one pound designed to trigger a buy-out clause alleged to have been written into the player's contract - something the Merseyside club also deny.
Purslow told Sky Sports News: "What's unusual about this case is there seems to be some significant confusion between the player and the club as to whether he did or didn't have such an escape clause.
"Yesterday [Thursday] it became clear that he did not have a clause, so I suspect he's pretty unhappy with his agent who got that wrong a year ago.
"I also suspect Arsenal are unhappy because they're a club who do their business extremely properly and professionally and they will have been made aware by intermediaries acting for the player that he thought such a clause existed.
"They will have done the right thing which is make a written offer to Liverpool.
"They may have spent a lot of time thinking that if they were to make an offer at that level they would be securing a player. This is not something one does on a whim.
"I suspect Arsene Wenger and Arsenal have been planning Luis Suarez as their main signing for some time and to discover that such a clause is not valid and doesn't work runs the risk of seriously wasting Arsenal's time as well."