The midfielder is on a season-long loan at Villa with an option to buy - which will not be picked by the Villans.
With Elliott not in manager Unai Emery's plans - and also unwanted by Liverpool - the midfielder's value is set to plummet ahead of the summer market.
Speaking on the Football Boardroom podcast, Purslow said: “The deal that was done, maybe by (former Villa transfer chief) Monchi and not by Unai Emery, has a perverse incentive for Unai not to pick the footballer.
“That is utterly and completely dysfunctional. Nobody benefits. Common sense would suggest compromise is required. You have a quiet word with the two sides and try to get them together.
“Unai needs to get together with the key player on the Liverpool side. This is Michael Edwards level - he is the CEO of football. He believed he had sold Harvey Elliott on a deferred transfer and it hasn't worked out.
“Unai and Michael in a room. Unai would say 'He's not going to play because we do not want to buy him.'
“If I were Unai, I would say 'If I didn't have this contract hanging over my head, there is a really good chance Harvey would get plenty of football between now and the summer.’
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“I believe that if the three parties all agree, they could modify the agreement. Liverpool have plugged into their financial models that they will receive a transfer fee for Harvey next summer but he is not going to be bought by Villa.
“If I were Michael Edwards, I would think that if he gets more minutes at Villa between now and the end of the season, his value will be maintained higher. But if he doesn't play football for a purely contractual reason for the next four months, everyone loses.”