Top seed Djokovic comes into the clay-court tournament, where he has been champion six times, braced to lose top spot in the world rankings to Alcaraz.
The flamboyant Spaniard, fresh from back-to-back clay titles in Barcelona and Madrid, just needs to play a match in the Italian capital to return to the summit ahead of the French Open which starts later this month.
"He's going to be number one after this tournament and if it happens it will be deservedly so. He plays very impressive tennis, a great level. He's the player to beat on this surface no doubt," said Djokovic, who starts his title defence against Argentina's Tomas Etcheverry (23) on Friday.
Djokovic won a record-equalling 22nd Grand Slam at the Australian Open in January but missed the American hard-court swing in March due to his refusal to be vaccinated against Covid.
He has endured a tough start to the European clay-court season, being eliminated in the last 16 at the Monte Carlo Masters, in the quarter-finals at Banja Luka and then pulling out of Madrid with his elbow problem.
However, Djokovic said that he had overcome the physical problems which have blighted this part of his season.
"It's all good, it's all good. There are always some things here and there that bother you at this level," he added.
"It's normal. When you're not 20-25 anymore you experience that a bit more than what used to be the case.
"I feel good... Historically throughout my career Rome has been a very nice tournament for me, I had success in it many times, got to finals.
"It's my most successful clay court event. Coming into the French Open it can be a great springboard for what's coming up in Paris where I want to be at my best."
