Clyne was picked for the Three Lions for the majority of their Euro 2016 qualifying campaign, but faces a fresh challenge from a rejuvenated Kyle Walker.
Walker missed the 2014 World Cup through, with Glen Johnson selected as starter as the Three Lions crashed out at the group stages.
Clyne's performances for Southampton earned him a call-up for England while Johnson was dropped, and he joined Liverpool last summer and has impressed since.
Walker missed the first part of last season through injury and when he returned he was out of form and looked far from England quality, but this season has been a different story.
He has been excellent for Tottenham, helping them to second place in the Premier League heading into April, and while Mills is impressed with the defender, he maintains Clyne is the better option.
He said: "In my old position at right-back, Kyle Walker has performed really well this season but I’d probably go with Clyne. Defensively, he’s very good."
Mills played at World Cup 2002 with England, and is less convinced about the other full-back position. He said: "Left-back is probably more of an issue. Shaw’s injury means he’s played very little football and is a question mark.
"Baines and Bertrand both have good shouts, as does Danny Rose but I wouldn’t say there’s been an outstanding English left-back this season who has nailed down the position in the way Ashley Cole used to do."