Scottish actor Capaldi is appearing in his final series as the Doctor.
He has said whoever replaces him - whether a man or woman - will be "wonderful".
Inverness-born Gillan, who played Amy Pond alongside Matt Smith's Doctor, said she would respect whatever decision was made on the role.
A man has been chosen as Capaldi's successor, according to newspaper reports.
Speaking at the Los Angeles premiere of her latest film, Guardians Of The Galaxy Vol 2, Gillan said: "It's OK, maybe next time.
"I trust the BBC and their choices and they haven't failed us yet with the Doctor.
"But it would be cool to see a woman in the role one day because a woman could absolutely play that role."
The BBC said no casting decisions have been made.
In Guardians of the Galaxy Vol 2, Gillan plays blue-skinned space pirate Nebula.

"Costs have got out of control, we need costs to come right down," he told BBC 5 live's Wake Up to Money programme.
Lord Browne said companies would have to "slim down", warning "there will be some companies that go to the wall".
The warning from Lord Browne, who led BP for 12 years, comes amid fears the industry is in crisis.
A barrel of Brent crude has more than halved in price since its peak of $115 last summer. On Tuesday, the price stood at $57 a barrel.
Last month, the chairman of the independent explorers' association Brindex told the BBC the industry was "close to collapse".
Robin Allan claimed almost no new projects in the North Sea were profitable with oil below $60 a barrel.
In recent weeks hundreds of North Sea jobs have been cut by oil firms, including BP and Talisman Sinopec.
The chancellor has said he will look at new measures to support the industry in his next Budget in March.
Both industry leaders and the Scottish government are calling for taxes to be cut further as a matter of urgency to help the sector deal with falling oil prices and higher costs.
Unions have also raised safety concerns over the number of job cuts being made in the industry.

The number eight made his comeback from a knee injury last weekend, and is included in a 24-man training party to prepare for the Calcutta Cup match.
Vunipola has been lined up to replace Nathan Hughes in the starting XV.
Scrum half Ben Youngs, wing Jack Nowell and centre Jonathan Joseph are also poised for returns to the backline.
Vunipola made his comeback ahead of schedule for his club Saracens on Sunday, after three months out with ligament damage.
And England head coach Eddie Jones appears set to bring him back at the first time of asking, after England's training plans on Tuesday showed Vunipola would start in the back row.
Bath centre Joseph, who was left out of the squad that beat Italy, is set to replace Ben Te'o at outside centre, while it's likely Youngs will be preferred to Danny Care, with Nowell edging out Jonny May.
England will confirm their starting XV and replacements on Thursday morning.
Jones' side lead the Six Nations table with three wins from their three matches.
Forwards (13)
Dan Cole (Leicester Tigers)
Jamie George (Saracens)
Dylan Hartley (Northampton Saints)
James Haskell (Wasps)
Nathan Hughes (Wasps)
Maro Itoje (Saracens)
Joe Launchbury (Wasps)
Courtney Lawes (Northampton Saints)
Joe Marler (Harlequins)
Kyle Sinckler (Harlequins)
Billy Vunipola (Saracens)
Mako Vunipola (Saracens)
Tom Wood (Northampton Saints)
Backs (11)
Mike Brown (Harlequins)
Danny Care (Harlequins)
Elliot Daly (Wasps)
Owen Farrell (Saracens)
George Ford (Bath Rugby)
Jonathan Joseph (Bath Rugby)
Jonny May (Gloucester Rugby)
Jack Nowell (Exeter Chiefs)
Ben Te'o (Worcester Warriors)
Anthony Watson (Bath Rugby)
Ben Youngs (Leicester Tigers)
Former Doctor Who companion Karen Gillan has said an actress succeeding Peter Capaldi in the lead role of the long-running TV series "would be cool".
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Former BP chief executive Lord Browne has warned North Sea oil operators' costs must fall in order for them to compete globally.
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Billy Vunipola will feature against Scotland in the Six Nations on Saturday, after being confirmed in England's matchday squad.