Spurs are on the lookout for a backup striker for Harry Kane in the summer transfer window.
And King is the latest name that has come up in the British papers.
Robinson thinks the attacker, who has 48 Bournemouth goals in 163 games, would play for the North London club.
"I played with Josh King at Blackburn and he has developed hugely as a player," Robinson told Football Insider.
"He came as a wide player after a very good academy upbringing. He was a talented player but he was not the finished article.
"I think he has got better and he now prefers to play down the middle. He has grown in stature and increased his physique. His speed used to be his real asset but now he has got end product as well.
"I can certainly see him fitting into one of the [Premier League] top-four's squads.
"If Harry Kane is fit, he plays, but he has not played a full season in years.
"He [King] is guaranteed games even if he is not a starter."