The defender has been given permission to play in the FA Cup, with his loan expiring after the date of the fourth-round ties.
Tate has made nine appearances since joining from the Swans and Leeds United manager Neil Warnock was pleased to secure his signature for a further period.
The Leeds boss said: "We've extended his loan until the 26th.
"That gives us some breathing space and there's time before the transfer window closes. We'll see how that goes."
Jerome Thomas has returned to West Bromwich Albion upon completion of his loan spell, and Warnock said nothing has been sorted regarding his future with Leeds.
He added: "It may be either a permanent deal or nothing I think.
"One or two other clubs are sniffing so we'll see what happens with that one."
Michael Tonge's loan spell also ended before the Christmas period, and Warnock confirmed that talks with Stoke City will continue with a view to his future.