Goalkeepers from Paris Saint Germain, Atalanta and Chelsea feature.
According to the Sun, they are looking to spend as much as £40million to lure the England number one to Goodison Park.
The Blues are in need of a new 'keeper considering Tim Howard has departed and Joel Robles struggled to assert himself when given the chance.
£40million would be a huge price to pay for Hart, especially given that he has not been without criticism himself in recent years.
There are other options available at a better price and we have compiled three that Everton should consider.
Asmir Begovic - Chelsea
The Bosnian keeper finally secured a move to a big club last summer after several impressive years at Stoke City.
It did not work out well for him though, and his side struggled in the first half of the campaign and eventually sacked Jose Mourinho because of it.
He is unlikely to be number one should Thibaut Courtois remain and stay fit, and a move to Goodison Park would make a lot of sense.
Marco Sportello - Atalanta
Sportiello is highly rated in Italy, having impressed with Atalanta since becoming their first choice last season.
Indeed, there is already interest in the Premier League with Bournemouth and Liverpool having been linked last year.
At 24 there is still more to come and he could prove to be a smart purchase.
Alphonse Areola - Paris Saint Germain
Areola is currently at Paris Saint Germain but he has spent the season out on loan at Villareal in La Liga.
He impressed with the yellow submarine, keeping 15 clean sheets in total, the third highest tally in the division behind Jan Oblak and Claudio Bravo.
He is unlikely to break into the first-team at PSG though, with Kevin Trapp the number one there, and he could be tempted by a move to Goodison Park should they be open to a sale.