With his deep pockets - no one tennis player in history has earned more than his US$108 million prize-money - Djokovic is perfectly placed to attract a big name such as Agassi, who has devoted much of his retirement to setting up charter schools in the US.
In a recent interview, Agassi was asked if he would consider returning to the tour, perhaps as coach of Nick Kyrgios. "I would not have any room now with my kids, who are 15 and 13," Agassi replied. "So the answer is no. I couldn't do it the way I would need to do it."
But this is where Djokovic has an advantage. As one of the big beasts of the tennis tour, he could offer the option of a consultant-type head coach role, which might involve only 10 to 12 weeks a year on the road.
While Agassi's early career was more turbulent than Djokovic's, he is well placed to understand the feeling of lassitude that can grip a tennis champion after years of achievement.
Agassi climbed to world No1 for the first time in 1995, and won Olympic gold in Atlanta the following year. But his ranking slipped to No141 in 1997 as his marriage to actress Brooke Shields began to fail. This was also the year when he tested positive for crystal meth, although he escaped without penalty after claiming that the ingestion had been accidental.
Yet Agassi regained his motivation with a vengeance, reclaiming the top spot in the rankings in 1999 and claiming five more major titles before his results began to fall away in his mid-30s.