"That's what I'd do," said McGeechan, who coached Cipriani during his time as director of rugby at London Wasps.
"Danny can run, he can kick and he'll enjoy that extra space."
McGeechan played Cipriani at full back during his debut season in first-class rugby three years ago as he attempted to bring him into the senior reckoning without overburdening the youngster with the extra responsibility associated with his favoured fly-half role.
With former double Lions tourist Jonny Wilkinson looking set to wear the No10 shirt for England following a series of impressive displays following his move to France, Cipriani's chances of making his country's matchday 22 appeared minimal before Armitage's injury.
The 21-year-old missed out on a place in Johnson's Elite Player Squad and is currently languishing in England's second-tier environment with the Saxons.
But with Olly Morgan now the only specialist full back in the EPS following Armitage's shoulder injury, Cipriani is one of a number of options for Johnson to consider ahead of the November internationals against Australia, Argentina and New Zealand.
If Johnson decides against using Gloucester's Morgan, he could instead opt for utility back Matthew Tait of Sale or either of the wing duo of Mark Cueto and Ugo Monye.
Tait is being viewed by his club as an out and out centre, however, and, although Monye is currently playing full back for Harlequins, both he and Cueto are far more experienced out wide rather than as the last line of defence.
Outside of the EPS, Johnson may favour Bath's Nick Abendanon or Northampton's Ben Foden but, as far as McGeechan is concerned, the door is now open for England's most-prodigious talent to once again prove his worth on the international stage.