According to Italian sources via Goodison News, Everton are keen on the Brazilian who flopped at their neighbours Liverpool two seasons ago and played very little for Jurgen Klopps team.
This is a slightly strange transfer rumour and appears to have come a little out of left field, although there were other suggestions the Blues might be interested in Melo.
On paper the 27-year-old is a strong defensive midfielder who spent last season on loan at Fiorentina from his parent club Juventus and made thirty three Serie A appearances for the Florence club.
On the face of it, he would seem to fit the mold of the type of player Sean Dyche is generally keen on and so there is some sense perhaps in the links to Everton.
It is very likely that at least one of Dyche's midfielders, Amadou Onana, will leave the club this summer as the Toffees try to balance the books and avoid another potential PSR breach.
That would leave the manager a little short of numbers in the middle of the park.
Having said that the Blues do still have the older heads of Idrissa Gueye and Abdoulaye Docuoure, at least for one more year and also James Garner.
Melo's time on Merseyside with Liverpool was not a success and so it is difficult to know how he would fare again in England. He has since gone to Italy and made a better fist of things there.
In addition, there are other younger players who might represent a better bet for the Blues as Dyche tries to build a more youthful squad for the future.
So, I am not sure the Brazilian midfielder would represent a good deal for Everton.
Perhaps instead the club should look to those younger talents who can grow and develop further, especially with the experience of Gueye and Doucoure already at the club.
At any rate Melo would I presume be a loan deal of some sort rather than a permanent signing at this time.
All of this may also directly depend on whether Dan Friedkin is able to complete his takeover of the Toffees soon, or if it will take much more time as there are conflicting reports about this.
If the American billionaire does succeed and soon in his objective, then given the 59-year-old's wealth the Blues may well be shopping in a different market than we are currently focussing on.