Everton forward Kevin Mirallas has hinted that he will sign a new contract at Goodison Park in the summer.
PSG president Nasser Al-Khelaifi says he would not even look at a £35m offer from Manchester United for Edinson Cavani.
The Italy international moved to the Stadium of Light in the summer of 2013 from Serie A champions Juventus.
The 29-year-old’s debut campaign in England was a struggle at times, with inconsistency blighting his game.
Another move was mooted over the summer, but the transfer window closed with the winger still on Wearside.
He has worked hard over pre-season and the early weeks of the campaign to put himself in Gus Poyet’s plans and claims to be enjoying his time in the Premier League.
Giaccherini said after Italy’s friendly victory over the Netherlands in midweek: “I feel good in England because I think the Premier League is the most beautiful in the world at this moment.
“But you can never say never because there is still homesickness.”
Giaccherini has also been reluctantly discussing his omission from Italy’s World Cup squad, with his performances in 2013/14 resulting in him being overlooked.
He added: “I would prefer not to talk about it. I have said many times that I was upset.
“I’ve accepted the decision of the coach because I have to show respect.”