Stoke's director of football John Rudge said: "We have taken Brynjar initially on a month's loan so that he is eligible to play this weekend but it is with a view to taking him permanently until the end of the season."
Stoke face high-flyers West Bromich Albion this weekend whilst Forest face a tough trip to Pride Park in the latest East Midlands derby.
David Johnson could make his first start since breaking his leg in September 2003 but Marlon King and Alan Rogers face suspensions. Des Walker is out after he limped off against Burnley in midweek with a hamstring strain but Matthieu Louis-Jean should be fit after coming off in the same match.
Derby striker Noel Whelan could partner new loan signing Paul Peschisolido upfront and Forest fan Michael Johnson could return in central defence.
Derby's key midfield man Leon Osman is a late fitness test though after suffering a dead leg against Watford.