Giannakopoulos signed a new three-year contract with the club to end mounting speculation that he was on the verge of a move to either Liverpool or Manchester City.
And the Bolton chairman Phil Gartside, speaking after the Trotters drew Lokomotiv Plovdiv in the first round of the Uefa Cup, confirmed that talks were ongoing with Tudor in a bid to agree personal terms with the 27-year-old who can play in defence or midfield.
Gartside said: "We have agreed it with Juventus and we have been talking to the player. It's just a question of getting him to Bolton and telling him what Bolton is all about. He has three years on his contract and Juventus are not keen to let him out on a permanent deal but they are quite prepared to let him out on a loan basis.
"However we have a good record whether they are permanent or not that when we bring a player into the club it's very rare that they leave. Even with our loan players within a year they have always signed and carried on playing."
The news that Bolton were closing in on Tudor came after the new Giannakopoulos contract which will delight Allardyce. Only two days ago, after the player had scored in the midweek win over Newcastle, the Bolton boss admitted that he was "not confident" of keeping his man.
But yesterday morning Allardyce revealed that his club had tabled a much improved offer which the 31-year-old was delighted to accept. Allardyce said: "We have been working hard behind the scenes to get this agreed and I am delighted.
"Throughout, Stelios has been very professional and he can now look forward to playing his best football for Bolton. I was concerned earlier this week but in the end he always wanted to stay loyal to me and the club.
"He is a terrific little player and a real match winner." Allardyce had grown increasingly frustrated in recent weeks over rumours of the player's imminent departure to one of his side's Premiership rivals. Bolton had rejected an initial £1m offer from Manchester City out of hand but then seemed set to lose Giannakopoulos when the Liverpool manager Rafael Benitez expressed an interest.
However there were clear signs of a change when Allardyce said the chances were "bigger and better" of keeping hold of the player. Allardyce had said: "He tells me he has always wanted to stay and now we have come with an offer which matches his terms. I want him to stay, the lads want him to stay and he says he loves the place."