Both Barrett (pictured) and Edwards have penned new one-year contracts at The Racecourse Ground as the Welsh outfit prepare for life back in Division Two.
Midfielder Barrett has decided to extend his four-year association with Wrexham while wing back Edwards arrived from Swindon last summer.
Veteran defender Carey and Northern Irish midfielder Whitley have both concurred on the terms on offer and are poised to sign their deals.
The pair are the only members of the squad yet to sign up for next season but Dragons chief Denis Smith is not perturbed by the situation dragging on.
"Both have given me verbal assurances that they will sign and as senior players on the team, I'm happy to accept their word on the matter," Smith told the club's official website.
"Obviously, it was good to get the deal with Eddie completed, especially as he was given the all-clear following a scan on his ankle."
