Several International Olympic Committee members called on Sunday for President Thomas Bach to stay on after his second term ends in 2025 and continue for an unprecedented third one.
Elected in 2013, Bach is due to step down in 2025 in line with current Olympic Charter rules, following a first eight-year term and a second four-year one.
The IOC, however, said it would be discussing the matter in a future executive board meeting.
Sunday's open declaration by IOC members followed speculation in recent months that Bach could potentially continue as president of the one of the most powerful bodies in global sports.
So far no IOC member has declared an intention to run for the top job, though there are several who are seen as potential candidates.
The number of terms was limited to avoid lengthy tenures such as that of former president Juan Antonio Samaranch, who was in charge for 21 years from 1980 to 2001.
"You have shown us the best way to go forward," IOC member Luis Mejia Oviedo told Bach as he proposed him for a third term.
"We have to look after this movement. That is why I would like to put forward this approach."
Several other members also called on Bach to stay on and asked for a Charter change.
It will not happen during their meeting in the Indian financial capital, as such changes need to be proposed in writing and handed in 30 days prior to an IOC session.
Bach, a German lawyer, said he was deeply honoured but refused to say if he planned to stay and whether he would propose a Charter change in future to make that possible.
"You know I am very loyal to the Olympic Charter. Being a core author of this Olympic Charter drives me to be more loyal to this Olympic Charter," Bach said.
"These words of support are not only directed to me. They are directed to all of us. What made us to overcome the challenges we had was exactly this unity," he said.
The next scheduled IOC session is in Paris just before the start of the Olympics Games next July.
Since taking over, Bach has had to tackle a number of major crises such as the Russian doping scandal following the 2014 winter Games in Sochi.
He also had to co-ordinate postponement of the Tokyo 2020 Olympics by a year due to COVID-19 as well as the fallout on world sport from Russia's invasion of Ukraine.
The former Olympic fencing champion has also pushed through many major reforms aimed at making the bidding and organising for the Olympics less expensive and complicated, and more attractive, for future host cities.
The IOC said the matter of any presidency term would now be taken up by the executive board at its next meeting.
"When members make a point it needs to be fully considered," said IOC spokesman Mark Adams. "They (points) will be discussed later on in a considered manner, as they should be."
"There are a number of members who make a point, some representing large constituencies," Adams added. "It would be strange if we were to deny members, trying to raise a point."