Patel, who took over as Chief Minister in May 2014 from Modi, will cross the age bar of 75 years on November 21 this year as she was born in 1941.
"This question about Patel, when she turns 75 is on everybody's mind," said a BJP leader on the condition of anonymity.
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"Speculations are on if she will be asked to quit or will she be an exception and allowed to continue for one more year till 2017 Assembly polls," another leader, who also refused to be named, said.
Heptulla, who crossed 75 years was reportedly asked to submit her resignation due to the age bar.
Earlier, a couple of ministers in Madhya Pradesh including senior leader Babulal Gaur and Sartaj Singh were dropped from the state Cabinet by Chief Minister Shivraj Singh Chouhan due to the age bar.
In 2014, when the Narendra Modi government came to power, the age bar had cancelled out ministerial berths for senior leaders like L K Advani, Murli Manohar Joshi, Shanta Kumar and Yashwant Sinha.
Sinha had in the past remarked that BJP has "declared brain dead on May 26, 2014" its leaders above the age of 75.
Under the leadership of Patel, who has been a minister in the BJP government since 1998 and CM from 2014, the BJP for the first time in the post-Narendra Modi era in Gujarat is facing a tough challenge from its opponents.
Elections in the state are due in the later part of 2017.
Patel had to face defeat as BJP recently fared badly in the rural civic bodies polls in December 2015.
This was considered as a major loss for her as opposition Congress was able to win polls after almost 25 years in the state.
She also had to face the fierce Patel community quota agitation, one of the factors which contributed to BJP losing in rural local bodies polls, while retaining urban areas. Opposition Congress has also leveled allegations of corruption against her.
No BJP leader was ready to speak on the subject officially saying that this could be "just a speculation".
The Congress however believes that this rule is followed according to the convenience of top leadership of the BJP.
"This is the internal matter of BJP. But, we believe that this rule is followed as per the convenience of the party leadership. If they want to keep someone then they do it and if somebody is to be removed the rule is followed," Congress spokesperson Manish Doshi said.
"Due to UP elections they have not taken the resignation of Union minister Kalraj Mishra. However, when they wanted to keep Advaniji and Murli Manohar Joshi out of the cabinet they followed that rule," he added.