Toffees boss Roberto Martinez is reported in several newspapers to be weighing up a move for the 23-year-old.
Scouts from Goodison Park have watched the Dons midfielder a number of times this season.
Jack has made more than 170 appearances for the Dons, scoring nine goals in the process. He was named SPFL Player of the Month for December 2014 and is tied to the Pittodrie club until summer 2016.
Derek McInnes is keen on keeping Jack at Aberdeen, who have secured a top two finish for the first time in over 20 years.
But Martinez has been keeping tabs on the Scottish market and with contract talks with Jack on hold until the summer, McInnes will be aware the Dons will need to cash in on the midfielder if he refuses to sign a new deal.
Source: The Scotsman