The 84-year-old will visit Scotland for the first time in November, in one of his first major public engagements since he had colon surgery in July.
He is expected to address the conference and meet with Scottish bishops, but sources have said the Pontiff also wishes to hold a public Mass.
"While the Pope is saying Mass is not 100 per cent confirmed, we have had word that he wants to do it and that’s why people are looking at the practicalities, such as a venue and timing, depending on the rest of his pretty tight schedule,” the source told the Mail on Sunday.
"It would have to fit in with his address to the conference and his meeting with the bishops.
“There is some doubt about whether it can be fitted in, but the Pope says Mass every day and would like to say a Mass for the people of Scotland.
"It’s not absolutely confirmed, but he wants to do it, and if the Pope wants to say mass for the Scottish public, there is going to be a huge desire to make it happen.”
A possible Mass would follow those given by Pope Benedict XVI at Bellahouston Park in Glasgow in 2010, and by Pope John Paul II at the same venue in 1982.
Pope Francis has recently been recovering from surgery in July to remove a portion of his large intestine at the Agostino Gemelli Polyclinic in Rome.
He made his first public appearance since the operation on July 11, speaking to crowds from his hospital balcony in Rome.
In response to well wishes from the Bishops’ Conference of Scotland, Pope Francis confirmed a few days later that month that he would attend COP26 so long as his health permits.
A spokesperson for the Bishops’ Conference of Scotland said: “Having written to the Holy Father to assure him of a warm welcome, should he attend the conference, they are delighted to hear that he does hope to attend and would be glad to meet with them in Glasgow.”
They added that at that time a large gathering was not planned for the Pope’s visit.
“The Pope will be in Scotland for a very short time, most of which will be spent participating in the COP26 Conference,” they said.
"While many pastoral, ecumenical and interfaith gatherings would be desirable while he is with us, time constraints sadly mean such a full programme will not be possible.”
Police Scotland is preparing for protest activity relating to the climate conference.
Deputy chief constable Will Kerr said the right to protest would be balanced against the rights of the wider community.
The Pope’s attendance is set to present one of the major security challenges around the conference, alongside visiting heads of state and the Prince of Wales.
The official proceedings are expected to attract around 30,000 delegates.