But they face competition from La Liga’s Real Betis, who are also in for the 31-year-old Sion captain.
The far-travelled stopper, who can play at left back or central defence, is out of contract at Sion in his homeland and wants a new challenge.
And he’s revealed in a Swiss newspaper he’s weighing up a move to the Scottish champions.
Asked if Celtic and Betis had offered him a deal, Ziegler said: “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.”
Ironically, Ziegler may have played a part in Hoops manager Brendan Rodgers getting the sack at Liverpool!
Ziegler launched a blistering attack on his Liverpool side after a Europa League 1-1 draw against Sion in 2015, accusing them of being ‘mentally weak’ after they had previously won just one of their last eight games.
Two days later, the Anfield giants axed Rodgers.
Ziegler has played in Switzerland, England, Italy, Germany, Russia and Turkey and has played in the past two World Cup for his countries.
He was at Spurs as a teenager after being snapped up from Grasshoppers by former boss Jacques Santini, but left ten years ago after losing his place to Gareth Bale, after loan spells at Hamburg and Wigan.
He moved to Sampdoria permanently after another loan spell, but switched to Juventus in 2011.
However, his spell at the Turin giants was a disaster and he never kicked a ball for them. He embarked on further loan spells to Fenerbahce, Lokomotiv Moscow and Sassuolo.
Ziegler has spent the last three seasons at Sion and is regarded as one of the most consistent performers in the Swiss Super League.
Now he could be set to be Celtic’s first incoming recruit of the summer.