However Sir Tony, who played Baldrick in all four series of the sitcom, joked that they might struggle to pay Hugh Laurie, who went on to become a major star in the US with hit drama House.
Comedian and television presenter Sir Tony, 69, told The Sun: “I do think a new series of Blackadder is on the cards.
“I have spoken to virtually all the cast about this now.
“The only problem is Hugh’s fee.
“He’s a huge star now - or so he’d like to think.”
Laurie is believed to have been paid as much as £250,000 per episode of House, which ran from 2004 to 2012, at its peak.
The hospital drama, loosely based on Sherlock Holmes, saw him adopt a convincing American accent to play the curmudgeonly but brilliant medic at a hospital in Baltimore.
Before that he was a successful comedian, mostly alongside fellow Blackadder star Stephen Fry in programmes including their own sketch show and ITV’s adaptation of the Jeeves And Wooster novels by PG Woodhouse.
Blackadder starred Rowan Atkinson in the title role, before he went on to star in Mr Bean.
Its historical settings spanned Medieval England, the reign of Elizabeth I, the era of Prince George IV and the First World War, with the latter’s final episode one of the most celebrated in the history of British comedy, featuring a poignant final episode in which the whole cast dies during a battle scene.
It finished in 1989, though a special episode, Blackadder Back And Forth, was made for the Millennium Dome in 1999.
Sir Tony, who went on to host Channel 4’s Time Team for 20 years, told The Sun: “Expectations for a new series will be high because people not only remember the original, they remember who they were when it was on.
“It’s a big danger.”