The high-profile couple reportedly rekindled their relationship last week after a brief split.
But Aoibhinn (28) is believed to be concerned about attending the unveiling of Tubridy's JFK in Ireland in the Mansion House next Wednesday, as she does not want their relationship to be the focus of the event.
The presenter himself remains determined to keep his lips tightly sealed about his current relationship status.
The Late Late Show host (37) declined to confirm whether the his romance with the teacher and presenter is back on.
"I'm not discussing any of that," he said, despite recognising the public interest in his love life.
"I don't mind at all. I understand, but I'm just keeping my counsel on that," he said.
Just weeks after it was confirmed that he had ended things with Aoibhinn, the RTE presenter was spotted walking hand in hand with her on Dun Laoghaire pier last weekend.
An onlooker said the couple were out for a romantic stroll, quashing suggestions of a permanent split.
"They had big smiles for everyone they met," they said. "They looked together and happy."
But the couple clearly plan on keeping their rocky romance off the radar for now as Aoibhinn was not on his arm at the launch of the new EP by The Late Late Show's house band leader Paddy Cullivan last night.
Tubridy is the co-writer of the title track, We Are Where We Are, marking his first credit on a song. But he insisted it is likely to be his only foray into the music industry.
"Paddy is a pal and we would have conversations a lot over a pint of Guinness and sometimes I just let loose and rant; I didn't realise he was going to turn these rants into a lyric," he explained.
"That's me and songwriting done," he added.
Rumours that the couple split first began in early September, when he showed up to events without Aoibhinn, including Electric Picnic.
She was also absent when he attended Canadian singer Michael Buble's second concert in the Aviva Stadium with a group of friends.
Sources speculated that the presenter's increasing workload was a factor in the end of the romance, as it now encompasses the major part of Gerry Ryan's former weekday slot on 2fm, hosting The Late Late Show, and completing the book on John F Kennedy's visit to Ireland in 1963.
And Tubridy admitted that his schedule often leaves him "tired".