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The 17-year-old from Gloucestershire won the champion apprentice trophy in his maiden season this year.
Marquand has racked up 68 wins across the last 12 months, prompting his trainer Hannon to make the comparison with Moore.
"I think he could be a champion jockey one day," Hannon told BBC Points West.
"I would be amazed if he does not go right to the top, he is the name on everybody's lips at the moment."
Marquand's rapid rise has seen him nominated for the BBC Young Sports Personality of the Year 2015 award.
The jockey has been named on the final shortlist for the award, alongside gymnast Ellie Downie and para-swimmer Tully Kearney.
"What he has achieved is a little bit special," added Hannon. "He is a lovely guy and thoroughly deserves his success. He is very popular and he has endeared himself with everybody."
Hannon, who has 300 horses based at his stables near Marlborough, is the son of former flat jockey champion Richard Hannon Sr.
Moore has enjoyed great success under the guidance of Hannon and won the champion apprentice title in 2003.
Since then, Moore has established himself as one of the most respected flat jockeys in horse racing and was champion jockey in 2006, 2008 and 2009.
"Ryan Moore performs on the big stage and he is the best jockey in the world at the moment. He is so professional and the ultimate jockey and that's who you want to be," said Marquand, who will find out if he has won the BBC award on Sunday.
"It is a yard that is constantly in the limelight and it is big to be attached to somewhere like this."
Teenager Tom Marquand has been tipped to follow in the footsteps of three-times champion jockey Ryan Moore by his trainer Richard Hannon.