Everton sacked Roberto Martinez on Thursday afternoon after weeks of speculation following a second successive disappointing campaign for the Blues.
There have already been a number of names linked as potential replacements for him, with Koeman having been among those proposed.
And it seems there is genuine interest from Everton, who have made him their number one priority to take charge at Goodison Park.
They are willing to offer big money to tempt him to Merseyside too, with the Mirror claiming a £100million transfer budget will be proposed to him.
His wages will also be increased, as they will offer him in excess of £5million, which would more than treble his current pay packet.
They face a challenge to convince him though, with the same report claiming he has not indicated he interested in the switch as yet.
Instead, it seems he is desperate to make a return to former club Barcelona at some point and is reluctant to sign up to a long term deal because of that.