Steven Gerrard tried to sign defender for Rangers but he chose against Ibrox switch.
Clarke-Salter chose against a switch to Ibrox, snubbing Rangers in favour of a move to Dutch side Vitesse Arnhem.
The Chelsea youngster was part of England's World Cup under-20 winning side.
Clarke-Salter had a brief loan spell at Sunderland last season along with Rangers loanee Ovie Ejaria.
Gerrard reportedly met with Clarke-Salter at this summer's Toulon tournament where he was in action for England and the pair discussed a potential loan transfer.
Clarke-Salter preferred to move to Holland, following Mason Mount's success at Vitesse last season. He has just been called into the England squad.
Defence was clearly a priority for Rangers this summer, with Connor Goldson and Nikola Katic signed permanently.
Rangers signed Joe Worrall on loan from Nottingham Forest on loan and Gareth MacAuley on a free transfer.
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