"I don't know exactly the process, when the votes are happening, when the new CEO, all this stuff gets decided. But anyway (Kermode) should maybe be put back in the mix," Federer said.
"But then again I don't know if he would want to be after everything that happened. "Sometimes when these things happen, it is like, 'OK, I had a good run, and it's OK to go'."
Federer said that he was pleased that Gimelstob had stepped down.
"I think it's definitely the right move by Justin. He needs to go back and figure things out. There is no doubt about that," Federer said.
"And the Tour needs to keep moving forward in these challenging times and important times right now.
"I was speaking also to some of the players on the Council to get a feel where they were standing when everything was brewing and I'm happy that the decision was taken by Justin and that now we can move forward and really like learn from what had happened also."
Wawrinka had earlier written about how there has been a "worrying decline in moral standards" in tennis as "politics have overshadowed the action on the courts".
"I feel compelled to express my views on this regrettable period in our sport," Wawrinka wrote. "This episode has left many players, myself included, concerned about the direction tennis is heading in.
"There is no place in our sport for those who behave like Justin. The lack of responses from people involved in the game, particularly at the beginning of this saga, when he was charged last December, was alarming.
"This is a situation where silence amounts to complicity."
Federer was speaking at the Madrid Open as he prepares for his first clay tournament in three years. His announced schedule has him playing in Madrid as his only warmup for the French Open, which starts on May 26. However, Italian Open organiser Sergio Palmieri is hopeful he could add a trip to Italy to his schedule.
"Federer is entered to play, which is different from the last two years when he withdrew ahead of time," Palmieri said. "So the fact that he's entered means it's possible for him to play. It's impossible to predict, though. ... Knowing him, it's more probable that he'll come only if he's playing well."
While he is a four-time runner-up, Federer has never won the Italian Open — making it one of the few significant trophies he hasn't claimed.
"Playing three consecutive tournaments on clay at his age is complicated," Italian tennis federation president Angelo Binaghi said. "But I think it also depends on his results in Madrid."
Serena Williams is also set to return from injury at the upcoming Italian Open.
Williams has not played since withdrawing from her third-round match at the Miami Open in March with a previously undisclosed left knee injury. She hasn't played in Rome since winning her fourth title at the clay-court event in 2016, when she beat Madison Keys in the final.
- With AP
