The Argentine midfielder is out of contract next summer, and so far he has failed to agree a new contract with the Andalusians to stay beyond then.
If that continues to be the case in the New Year, he will be free to negotiate a deal with prospective new clubs from 1 February.
And that has sparked widespread interest in his services, with the Toffees among a number of clubs across Europe keen on signing the midfielder.
They aren't the only Premier League side interested in his services though, with Manchester United also reportedly keeping track of the situation with an eye to making a move.
However, both sides would face competition from Serie A, with both giants Juventus and Roma also reportedly interested in a deal for him.
Sevilla though, are still working hard to try and secure their star, who was key to their successes last season, to a new deal.
With such widespread interest in Banega, it seems unlikely that Everton would be able to compete with some of Europe's top clubs that are reportedly interested.
However, there is no denying that the Argentine would be an excellent addition to the midfield should we be able to secure him, with him representing a vast improvement on what Roberto Martinez currently has available.
Should the Blues be able to secure him on a free transfer as well, that would make a deal all the better.