Cole, who played wheeler-dealer Arthur Daley in the original show, claimed that the producers hadn't consulted him or co-star Dennis Waterman about the remake.
The original Minder aired on ITV for ten series between 1979 and 1994.
"Audiences remember Minder as me and Dennis, but neither of us has been given any input," he told The Sun. "They had the cheek to ask both of us to help them promote it though.
"They didn't offer either of us any money and we're not appearing in it, so we both gave them a resounding 'no'... I don't plan to watch this new series. It is on Channel Five after all."
Shane Richie, 44, and Lex Shrapnel, 29, star in the reimagining of the long-running British comedy drama, which begins on February 4.