Caretaker manager Kevin Dillon has publicly stated that he wants to take over from departed Alan Pardew on a permanent basis.
But since Pardew walked out of Reading, Dillon has won just once in three matches and the feeling is growing that chairman John Madejski will make an appointment from outside.
Dillon has applied for the job but faces tough competition after the chairman revealed that he had been "inundated with applicants".
Reading are expected to announce their choice early next week.
Things looked good for the Royals early on with striker Nicky Forster in stunning form.
It was no surprise when he put Reading in front after 21 minutes.
Defender Adie Williams chipped the ball forward to Forster who exchanged passes with James Harper before hammering a shot across the face of goal and inside the far post.
Coventry had made it clear that they were a threat when big Nigerian striker Dele Adebola hit the woodwork and it was Adebola who eventually hit Coventry's equaliser.
Michael Doyle sent in a left-wing corner which Steve Brown should have cleared easily. He completely miskicked and allowed Adebola the chance to beat Reading keeper Marcus Hahnemann.
Coventry were comfortably the better side after the break as Reading's passing let them down with several players performing well below their best.
Morrell had three great chances to put Coventry in front but put the first two over the crossbar and the third just wide of the upright.
His persistence was rewarded ten minutes from the end when a pass by Yazid Mansouri set him up for his third goal in three games.
Coventry's Gary McAllister said after the match: "That will set us up nicely for our midweek cup tie against Spurs."
Reading's Dillon said: "I hope the chairman judges me on my record over the past two years and not just on this game."
Reading: Hahnemann, Murty, Brown, Williams, Shorey, Murray, Sidwell, Harper, Hughes, Goater, Forster. Subs: Ashdown, Mackie, Watson, Tyson, Daley.
Coventry: Shearer, Shaw, Konjic, Staunton, Warnock, Mansouri, Safri, Doyle, Suffo, Adebola, Morrell. Subs: Arphexad, Whing, McAllister, Jorgensen, Barrett.
Referee: P Crossley (Kent)