The Premier League side are hoping to provide Seamus Coleman with some cover.
However, the Toffees are also keen on the youngster and have now sent representatives to keep an eye on his progress as they look to fill the void that they had hoped Sam Byram would step into before the Leeds United full-back decided to join West Ham during the January transfer window.
While Tudor is some way off being the finished article, he has the potential to become a fantastic player. His pace has often seen him used further up the pitch on the wing, and that has allowed him to score five goals in the league this year.
And while a move to Goodison Park is unlikely to see him initially earn the amount of first-team football that he has had at Hajduk, the opportunity to work alongside Coleman and see what has turned the Republic of Ireland international into one of the most impressive right-backs in the division will surely benefit his chances of realising his potential.