With Alexander Isak out injured, Gordon started as Newcastle's striker in their clash with Manchester City on Saturday.
The 23-year-old scored from the penalty spot and impressed with his work rate as Eddie Howe's side earned a 1-1 draw against the champions at St James' Park.
Amid the criticism Kane got for his performances in the Euros this summer, Cole says Gordon could be an alternative for England.
Speaking on TNT Sports, he said: 'I’ve been really impressed with him in this position and I think he gives you an option.
Anthony Gordon scored a penalty against Man City and impressed with his work rate
'I think from an outside looking at England I think that’s a food for thought for the manager because playing him there, the pressing was exceptional as good as a pressing performance I’ve seen from a No 9 I’ve seen in a long time.
'There’s not many that buy into it as much as he does and that set the tone. Newcastle were brilliant behind the ball, all of them, but. He was so important for them.'
Meanwhile, England under-21s coach Joleon Lescott believes the forward's best performances come from the left instead of as a centre forward.
'In terms of involvement, you probably get more involvement from Anthony on the left side,' the former Manchester City and Everton defender said.
'He's a winger that loves one vs ones but having worked with him for years now especially in the U-21s, he played as a No9 for us in the tournament.
'He was player of the tournament as a No 9. He’s someone who want to run in behind. I’ve never met someone that’s so enthusiastic about working as hard off the ball as he is in possession and you can see every actions there’s 100 per cent effort.'
Gordon was a frustrated figure this summer having played just a minute of England's Seven Euros games under Gareth Southgate.