Vaughan, 24, who scored 14 goals in 37 appearances for Huddersfield during a season-long loan, has returned to his parent club along with fellow loanees Jermaine Beckford and Neil Danns (both Leicester), and Theo Robinson (Derby).
Beckford, who netted nine times in 22 appearances for the Terriers, does not appear to be in Robins' long-term plans.
"It's hard to make these decisions so soon after the high of Saturday, but the club must start planning now for the 2013/14 season," Robins told the club's official website.
Striker Lee Novak, midfielder Oscar Gobern and Under-21 captain Jordan Sinnott are among those offered new deals, but forward Alan Lee, midfielder Scott Arfield and defender Tom Clarke have been released.
"Offers have previously been made to Lee Novak and there is an opportunity for him to stay here, if he wants to," Robins added.
"Alan Lee, Scott Arfield and Tom Clarke have all contributed really well to the club and it's never easy telling lads like them that they won't be part of the plans.
"Our loanees Jermaine Beckford, Neil Danns, James Vaughan and Theo Robinson return to their respective clubs now too having done ever so well for us, but we do plan to speak to Norwich City and James Vaughan about their respective plans."