King failed to make an appearance for United despite his promising reputation but has excelled under Eddie Howe at Bournemouth, scoring 48 goals in 163 appearances since arriving in 2015.
While Premier League clubs prepare for a return to action later in the month, Kane - who has not played since New Year's Day due to injury - has now returned to fitness.
Former Tottenham goalkeeper Robinson believes the presence of the England captain would not be detrimental to King, however, insisting the forward would still get ample opportunity to play if a move were to materialise.
“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.”