The pair, who had their first child at Christmas, are in the running for the prize to be awarded next month.
Also up for the title are stars such as James Corden, Jonathan Ross, Wayne Rooney and Gary Barlow.
The Premier Inn Celebrity Dad of the Year award aims to “reward the celebrity dad who has impressed the nation by balancing a hectic public life with the demands of parenting” according to organisers.
Sir Elton and Furnish announced they had become parents to Zachary, via a surrogate mother, in December.
Also on the celebrity dad shortlist are reigning champ Peter Andre, David Beckham, Jeff Brazier, Kevin Pietersen, Rod Stewart, Frank Lampard, Kris Smith, Michael McIntyre and Gavin Henson.
The winner will be announced on June 16, ahead of Father’s Day on June 19.