The Homeland and Supergirl star is among the actors whose names have been suggested to replace Peter Capaldi.
"It's nice to be in the running," he told BBC News.
"It needs to do something different, so I think it's either going to be a black person or a woman. It would just bring a different flavour to it."
The 51-year-old British actor has already been in Doctor Who, appearing in the 2009-10 double bill The End of Time. He can currently be seen playing the Martian Manhunter in the The CW's Supergirl.
"I'm already playing an alien so maybe I could switch and play a Time Lord - who knows what's going to happen," he said. "It's nice to be in the running. It's an iconic role."
The current bookmakers' favourite to take over the Tardis is Oscar-winning actress Tilda Swinton, and Harewood said she would be a good choice.
"She's extraordinary anyway so I think she'd be great," Harewood said. "It would be a very different Doctor and maybe that's what it needs."
The actor said it was good that four of the five current favourites are women - with Maxine Peake, Phoebe Waller-Bridge and Olivia Colman also tipped.
Harewood was speaking at the Independent Spirit Awards in California, where he was nominated for best male lead for playing a Pentecostal minister trying to perform miracles in Free In Deed.
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Actor David Harewood has said the next Doctor Who should not be another white man - and has thrown his own hat into the ring.