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.
Midfielder Hughes, who joined Aberdeen last January, has agreed a new 18-month deal, while full-back Naysmith has extended his contract until the end of the season.
Both players have established themselves as key players in Craig Brown's plans and the Dons boss is delighted to secure the experienced duo.
"Both players are happy to be at the club and we are happy to have them," said Brown.
Hughes is likewise happy to have penned a new deal until the end of next season.
"It is good to get the contract done," admitted Hughes. "I have a bit of security now and I feel there are good times ahead here."