Kenny Jackett is searching for a player who can give Wolves 'another 10 to 15 per cent in terms of quality'.
Neil Adams says Norwich remain in the market for further additions after signing Cameron Jerome and Carlos Cuellar.
The former Republic of Ireland international has been a major success since arriving on Teesside a month ago and will now stay at the Riverside until February 28.
Boro chief executive Neil Bausor said: "We are extremely delighted to secure the extension of Shay's loan until the end of February."
Given has played seven games for the Teessiders since making his debut against Bolton on November 30 and has kept four clean sheets. His arrival has coincided with Boro's best run of results since November 2012.
Given is the second most capped player for the Republic of Ireland, having played for them 125 times.
He made 461 appearances for Newcastle over a 12-year spell before moving to Manchester City on transfer deadline day in January 2009.
After making 69 appearances for City, Given moved to Aston Villa for a reported £3.5m in the summer of 2011.
Given is one of a select band of players to have represented all three major North East clubs, having also made 17 appearances on loan with Sunderland in 1996.