The Norway international has emerged as one of the decent strikers in the Premier League as he has scored 46 times since the South-Coast based team gained promotion to the upper echelon of English football.
King was close to joining Manchester United in the winter transfer window but the Cherries declined any possible move for one of their prized assets.
Robinson has tipped his former Blackburn team-mate to make a big move away from the Vitality Stadium when the transfer window reopens.
The 28-year-old has also been linked with a move to Tottenham Hotspur and Robinson believes King would be guaranteed game-time at Spurs regardless of Harry Kane's return to fitness.
In an interview with Football Insider, the 40-year-old Englishman revealed that the Norwegian has developed as a player since their time together at the Ewood Park.
“I played with Josh King at Blackburn and he has developed hugely as a player,” Robinson said.
“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 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.”