Speaking on the programme last month, Ms Phelan shared details about her battle with cancer and undergoing treatment in the United States, while Mr Bird who was on the show last Friday night, spoke bravely about his Motor Neurone disease diagnosis.
The two subsequently met up for "tea and scones".
Afterwards Ms Phelan shared the Twitter post in which she wrote: "The tea & scones have been had. The conversation flowed.
"We laughed. We cried. We hugged (apologies in advance to the Covid brigade!)
"We made plans to meet again.
"I have also been roped in to climb Croagh Patrick with Charlie & Claire and the whole of Ireland, it appears."
Journalist and disability rights activist Ms O'Riordan has now offered to join the hiking party too.
She took to Twitter yesterday, posting: "Hey @charliebird49/ @PhelanVicky I hear you are going for a hike up Croagh Patrick! Room for a limbless girl? My brother says he will carry me on his back if he has to #WithYouAllTheWay."
Responding to Ms O'Riordan's offer, Ms Phelan wrote: "Ahhhh Joanne, we would be delighted to have you join us," to which Ms O'Riordan responded: "Just give me a time and date, and I'll be there."