Everton director of football Steve Walsh is also reported to have scouted Dost last month when he played for Sporting Lisbon during a Champions League loss against Barcelona coming on as a substitute.
Everton have clearly been struggling in front of goal since Romleu Lukaku left the club this summer and it is likely that they will sign a new striker in January.
Meanwhile Sporting president Bruno de Carvalho said in May that his club would only sign Dost should they get a big amount of money.
He stated: "All I can do is confirm that I don't have the need to sell at this time. However, if I receive a crazy offer, I will accept. If I have a good offer, and the willingness of the player, we'll see."