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 Warburton seeks to strengthen his back line.
“Philippe has been first-class,” said the Rangers manager. “For a guy who’s been training away without a team, he looked fit and strong and his CV is very impressive.”
Lescott had agreed terms with the Ibrox club and was due to sign a two-year contract having negotiated his release from Villa, where he has one year left on his contract.
BBC Scotland understands that the move fell through over an issue raised by the player’s medical, although Aston Villa owner Dr Tony Xia claimed Rangers and the player failed to agree personal terms.
Warburton refuted this and said that Lescott decided that he did not want to move his family north.
“Let me be really clear about this – it’s absolute nonsense,” Warburton said.
“Personal terms were all agreed, but the player just decided to keep his family in Manchester. He’s well settled with three young children.
“It’s absolute nonsense to say anything other than that. The fact he’s up here tells you that terms were agreed and there wasn’t a problem with that.
“It’s a big decision on the player’s part and we understand that, but it’s nothing to do with what I’ve read in the papers.
“We know what happened, the player knows what happened.
“To take your three young kids out of school is a big call on his part and we respect it. It’s unfortunate, but we wish him all the best.”