Cole is training with Scottish Premiership champions Celtic at the moment with a view to joining them on a contract, as announced by manager Ronny Deila on Sunday.
The former Chelsea striker is a free agent at the moment, having left Premier League outfit West Ham United at the end of the 2014-15 season.
While Duffy rates the 31-year-old highly, he does not believe that the Englishman would be able to fit into Celtic manager Deila’s system.
“I don’t know how he would work in the current Celtic system,” the current Greenock Morton manager told The Scottish Sun.
“Ronny Deila likes to play 4-2-3-1, and I’d see Carlton as being best in one of the positions on either side, rather than as the one up top.
“I realise he won most of his England caps as a No9, where he had to deal with confrontations with defenders who were as big as him physically. But when he’s out wide he has the ability to glide past people.”
Duffy has also highlighted another reason for his surprise at the news about Cole training with Celtic, suggesting that the former West Ham man is not going to settle for a place on the substitutes’ bench at the Bhoys.
“The other snag I might foresee is that when players from down south come up to Scotland in their 30s they are viewed as being squad players,” said the 56-year-old.
“I don’t know if Carlton would settle for that, assuming Celtic try to sign him. He was still playing fairly regular football in the Premier League with West Ham last season.”
Celtic have three recognised strikers on their books at the moment - Leigh Griffiths, Nadir Ciftci and Anthony Stokes - and it seems that manager Deila wants to add one more.
Cole is a hugely experienced striker who started his professional career at London giants Chelsea.
In recent years, the Englishman has struggled to score goals, which raises doubts whether he will be able to break into Celtic’s starting lineup.
Last season, Cole scored two goals and created eight chances in 23 Premier League appearances for West Ham, while during the 2013-14 campaign he found the target six goals and created eight chances in 26 matches.
Back in 2012-13, Cole scored two goals and created 11 chances in 27 Premier League appearances.