The Bosnian international spent the second half of last season with Tony Pulis’s side, appearing 17 times for the club and scoring once against Derby County to help Boro make the play-offs.
The 25-year-old quickly became a regular through his hugely impressive performances at the Riverside Stadium and it is no surprise that he has been chased once again by the side who were beaten by Aston Villa over two legs in May.
The midfielder has played just 56 times for Everton since his £4.8m move to Merseyside from Hungarian outfit Ferencvarosi in the summer of 2014, largely due to a knee injury which saw him miss the entirety of the 2016/17 campaign.
Besic, who had also been linked with a transfer to Swansea City, is under contract with the Toffees until 2021.
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