The nine-year-old has won the Munster National at Limerick, the Ladbrokes Trophy at Newbury and a hurdle race at Leopardstown since joining Mullins from the now-retired Sandra Hughes.
Mullins trained Hedgehunter to claim a popular National success in 2005 and has 10 entries in total this time around.
Speaking at a special ceremony to unveil the weights at BAFTA in London's West End on Tuesday evening, Patrick Mullins, assistant to his father, said: "We are very happy with Total Recall. With over 11st it will be hard, but he has got that kind of an improving profile that makes him very interesting.
"He looks like a fantastic jumper, he handles big handicaps and he should stay.
"He is entered in the Gold Cup, but the form of his Ladbrokes Trophy win over Whisper probably puts him a good bit off that.
"The Bobbyjo Chase (at Fairyhouse) has been a lucky race for Grand National winners prepping (for Aintree) and they are two possibilities."
The £1million Grand National is the only handicap of the year when the British Horseracing Authority's heading of handicapping, Phil Smith, has absolute discretion to deviate from normal handicap ratings when determining the weights.
Smith has framed the weights for the world's most famous steeplechase every year since 1999, but this will be his 20th and final year in the role.
He said: "This is my 20th and final year of handicapping the Randox Health Grand National.
"It is a task that has got easier in some respects and harder in others. I have thoroughly enjoyed my time - it has been both a privilege and a pleasure to frame the weights for the great race.
"This year, 73 per cent of horses are in the handicap, compared to 67 per cent in 2017.
"In terms of getting a run on April 14, I would say you have a reasonable chance if you are in the top 70, which is down to 10st 2lb."