Premier League champions Chelsea signed Morata from Real for a club-record fee of £60m ($80m) in July after he spent the majority of the 2016/17 season on the Madrid bench.
Real forwards Karim Benzema and Cristiano Ronaldo have only scored two goals combined in their past eight La Liga games. Morata, in contrast, has scored eight times in 11 league appearances for Chelsea this season.
The 25-year-old chipped in with crucial goals for Madrid last season to help them win a league and European Cup double, and Gibson said club coach Zinedine Zidane should have given him more playing time ahead of Benzema to keep him happy.
Barcelona, Valencia, Real Sociedad and Celta Vigo have all outscored Real in La Liga this term, with the 12-time European champions playing out a goalless draw at Atletico Madrid last weekend.
"Morata is the elephant in the room for Real Madrid," Gibson told Sky Sports.
"He's five years younger than Benzema, was in better form last season and should've got more games."
Gibson said Ronaldo was struggling to replicate his goal-scoring performances of old as he was receiving the ball with his back to goal too often and suggested that a position change might serve him good.
"Ronaldo is 32, so they'll have to be in the market soon for another centre forward. There's a lack of movement from the front pair, and most of Ronaldo's goals in the last couple of season have been one-touch finishes," he stated.
"At the moment it doesn't seem to be suiting him with his back to goal. All the goals he scored, he was the final piece of the jigsaw, supplied service by a fantastic pass.
"I just wonder now if he's not entirely comfortable with his back to goal, and whether it might be an idea to put him back onto the left and change the system slightly," Gibson added.
Real are 10 points behind La Liga leaders Barcelona after 12 matches. They face Apoel Nicosia in Cyprus in the Champions League on 21 November.