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.
The 24-year-old Sporting captain will be out of contract in June and, according to the Primeira Liga outfit, has joined Reading in a 750,000 euros deal which includes a sell-on clause for a future transfer.
Carrico wrote a farewell letter on Sporting's website.
In it, he said: "It is with mixed emotions that I write this farewell message. I'm leaving the club of my heart, where I had the privilege of graduating (through the youth ranks) and serving for several years.
"I'm leaving because I understand that I am at a stage in my career when I have to take chances. Moreover, the proposed project is extremely exciting to me and know I can succeed."