The Three Lions are yet to appoint a full-time successor to Wayne Rooney, who retired from international football in August, with boss Gareth Southgate having rotated the captaincy in matches this year.
Cahill is one of the favourites to take on the armband, along with Tottenham star Kane and Liverpool's Jordan Henderson, all of whom are in the squad for this month's final World Cup qualifiers against Slovenia and Lithuania.
But Robson, who captained United and England during a glittering career, says it would be better to keep Kane free of the responsibility.
"I have never been an advocate of strikers being captain," Robson wrote in The Daily Mail.
"There is a clamour for Harry Kane to lead England and I understand that. He's scoring goals, full of confidence and works his socks off but I wouldn't make him captain.
"It needs to be a centre-half or midfielder as they are closer to the main action and in a better position to assess the team shape.
13 - Harry Kane now has 13 goals for club & country in September 2017; his best ever goal tally in a single month of his career. Unstoppable pic.twitter.com/Bt0mrkDJjP— OptaJoe (@OptaJoe) September 30, 2017
"The important basic in football is to stay switched on, it's all about what you do next. When a striker misses a chance there's a moment when his head may go down or he ponders what he should have done.
"Behind him, the team need to be in position to regain possession and a centre-half is best placed to shift people into place. Generally, that's not something a striker thinks about. That's why, for me, the captain should be Gary Cahill.
"I had Gary for a three-month spell on loan at Sheffield United when he was 21. Even then he was a good talker and organiser, and he's a quality defender.
"He's worked alongside one of the best captains in John Terry and has taken over his mantle at Chelsea. He's got experience, 57 caps, and when he talks to younger players he will command their respect.
"When I was England captain, my first concern was to get my own game right; only then can you encourage or criticise others – lead by example.
"Don't get me wrong, Kane can inspire those around him, but I'd leave him to concentrate on scoring."
England need only a point from their last two qualifiers to guarantee a place at the finals in Russia next year.