The 18-year old has been most impressive for the Toffees this season and his performances have not been lost on Round who believes he can become something special.
"He came into the team at the start of the season when we didn't have too many options and it was a case of 'needs must'; he was thrown into the big wide world of The Premier League," Round said in the Liverpool Echo.
"Over the course of the year, as he has got physically stronger and mentally matured, you can see he is starting to stamp his own authority on games and his qualities are coming through.
"I think we have got a very talented player in our ranks and he could go on to become something rather special; you saw that in the second half against Tottenham."
Round added that Rodwell is in line for selection for this month's FA Cup final against Chelsea despite his tender years.
"If he happened to get selected for the final, he would be up against [Michael] Ballack, [Frank] Lampard and [Michael] Essien. There is no hiding place in The Premier League. Once you cross that white line, you have got to deliver and your age isn't a consideration," Round added.
"But we believe in him and we believe he is ready. If he believes it as well, he could go right to the very top."