The 31-year-old normally plays as a centre-back or at left-back, and is available for free this summer after running down his previous contract at FC Sion.
A varied career has seen Ziegler play at the likes of Tottenham, Grasshoppers, Juventus, Fenerbahce and Wigan Athletic, and now it seems he could be heading for a surprise move to Glasgow.
Speaking via the Scotsman, when asked if Celtic had offered him a deal, Ziegler confirmed the move, saying: “That’s true. But before I meet with those two clubs, I will also meet with the people who run Sion to find out more.
“The offers from Celtic and Betis are an honour for me.
“But without wanting to sound snooty, I think I deserve it, I’ve had a good season.”
“I am getting married at the weekend and if I moved to Scotland, she would want to move abroad again with me I hope!
“But we are not there yet.”
Celtic are yet to sign any new players during the summer transfer window after winning last season’s domestic treble without losing a single match, and it seems Brendan Rodgers is keen on adding quality rather than quantity.
Patrick Roberts’ medium to long-term future remains up in the air, but what do you make of the move for Ziegler?
Is he the kind of experienced player who could help Celtic in the Champions League?
What do you think?