The former Irish international keeper was targeted by Coventry boss, Roland Nilsson, to help solve a keeper crisis at Highfield Road, after Hedman pulled his hamstring and reserve Andy Goram suffered a groin strain.
Branagan's representative Jeff Weston admitted: "Coventry spoke to Keith but it was only in case Hedman was not fit. They now think he will be fit, and Andy Goram is also rated as being 60/40 to return after injury for them. Coventry only wanted Keith if Hedman was not fit, so it is not going to happen now."
Meanwhile, Alan Kelly has asked to be taken off the transfer list at Blackburn Rovers.
Kelly has struggled to feature in the Rovers side since Graeme Souness arrived at Ewood Park two years ago and asked to be placed on the transfer list last season following his demotion to third choice keeper at the club.
The former Sheffield United keeper has been linked with moves to Manchester United and Spurs, as well as completing a successful loan move with Birmingham, but has now decided to stay at the Lancashire club and fight for his place.