Radcliffe, who held the world record for the women’s marathon for 16 years, was one of Great Britain’s top athletes who never enjoyed the best of fortune at Olympic Games.
She abandoned the 2004 Olympic marathon after 22 miles following a pre-Games injury, before experiencing more physical problems leading up to Beijing 2008 and later being forced to miss London 2012 with a foot injury.
Mageean has had similar poor luck with injuries ahead of the Olympics, and Radcliffe believes that she should channel her frustrations into her recovery.
The Achilles issue comes after Mageean won European Championships gold at the start of June.
“It is tough. Every athlete has their own way of dealing with that trauma. I like to deal with it and get it out there,” Radcliffe said.
“You cry, there’s a lot of frustration. When she is healthy she can go out and start to really smash it in training and put that frustration out there.
“Then you come back, at the next opportunity to get back into racing and show what kind of a class quality athlete she is.
“She knows the type of athlete that she is and she knows what she can produce when she is right.
“She has to go away now. Get all of that emotion out and come back strong for next year.”