Manager Mark Waburton says Rangers are considering a move for former Arsenal defender Philippe Senderos but will also assess other options.
The Ibrox club had hoped to sign Aston Villa centre-back Joleon Lescott, but that move broke down.
"We're looking at a number of options," the Rangers manager said following his side's 2-1 Scottish Premiership victory over Motherwell.
"Philippe is in with us, but it's important we make the right choice."
Senderos, who has left Swiss outfit Grasshoppers, spent four days training with Rangers, and is due to return to Scotland next week, as Waburton seeks to strengthen his back line.