Cook, who featured heavily for Worthing in their Ryman League Premier Division campaign last term, is currently on trial with the Shots.
Aldershot manager Gary Waddock cast his eye over the defender during their friendly with Championship Brentford last Friday and is keen to see more of what he has to offer.
Shots have already signed non-league forward Shaun Okojie from Corinthian Casuals, a team that played a division-lower than Worthing last term, this summer and Cook has impressed Waddock so far.
He told getsurrey.co.uk: "He's a centre-half, which is another position we are looking at. There are players out there but you just have to have the right contracts I suppose.
"Me and James [Rowe; Aldershot assistant manager] have seen Jack play first hand, so we know what he is capable of. It's a big step up for him but there is potential there."
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