Celtic claim a fee was agreed with Manchester City for John Guidetti prior to them taking the striker on loan.
Xabi Alonso claims no Premier League offers were put to him before leaving Real Madrid for Bayern Munich.
It means the 24-year-old Republic of Ireland international has extended his stay at Goodison Park until the summer of 2018.
"I'm over the moon. I'm glad to get it all done and to sign for so long at a club like Everton is a great achievement - I want to be here for as long as possible," he told evertontv.
"Signing a contract here is fantastic and I'm really looking forward to the next couple of years.
"I'm going to keep working as hard as I have done since day one and keep improving every day in training to impress the manager.
"I'm really happy to have signed for the length of time that I have."