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Shorey, known amongst Royals fans as 'Mr Dependable', is unlikely to feature again this season as he is suffering from an infection in his foot.
Gordon, who turned 31 last month, will wear squad number six and should make his debut against West Ham in eleven days time.
The Sky Blues, who are challenging for a top six place, have however insisted that their former Crystal Palace and Middlesborough man must not play against them at Highfield Road this Saturday.
The injury-ridden full-back has played under Steve Coppell before, he previously linked up with the Reading manager at Crystal Palace.
Coppell, who has been scouring the market for defenders as he bids to shore up his defence, revealed that he stumbled across the idea of signing Dean Gordon purely by fluke.
"I know him well from quite a long time ago, and by chance I saw him last week at a Coventry game I was watching, so that jogged my memory," he remarked to the official site.
"Realistically after the weekend we had half a dozen potential signings in that position, but the list quickly diminished and I was delighted when Coventry agreed to let him come to us, with the limitation of our game against them."
Gordon signed for Coventry last summer following a loan spell at Cardiff City at the back-end of last season. However, the Thornton Heath born defender has played just seven times for the Sky Blues this season having had his campaign affected by injury.
Gordon is Coppell's sixth signing, amongst those Lloyd Owusu, Ivar Ingimarsson, and Paul Brooker are players Coppell that have featured in the ex-Man Utd player's squads at other clubs in the past.