The Romanian international's performances at Euro 2008 have attracted the attention of clubs across Europe.
And Celtic are in pole position to sign the big centre-half, who is rated at around £3.75million.
His agent Cristian Morosan said: "Celtic approached me at the end of the European Championships to tell me they were interested in signing Gabriel.
"They weren't the only club who want him. He has options in England, Spain and Romania.
"But a move to Celtic certainly holds strong appeal to Gabriel. He knows they are a massive club who play in the Champions League every year. They have a vast support and on a sporting level would be a big step up for Gabriel."
It now appears Tamas has leapfrogged Watford stopper Danny Shittu to the top of Gordon Strachan's summer wish-list.