Perhaps this is not the player that the majority of Everton supporters would like to see move from the Etihad to the new Hill-Dickinson Stadium, where the Toffees will kick off the new campaign.
If one of Pep Guardiola's formerly all-conquering side were to become a Blue, then probably that would ideally be Jack Grealish, who has been repeatedly linked with a move to the Toffees over the last few weeks.
But while that possible deal might still happen, this story claims his England team-mate Walker has already agreed to become an Everton player after being left out of the Club World Cup by his manager at City, as Grealish has been too.
The paper says that the deal is all but signed and sealed with just a few key terms and conditions to be ironed out, most particularly whether Walker will join on a loan or permanently.
Walker has already been on loan over in Italy with Milan, where he played his football last season after losing his once almost guaranteed starting slot in Guardiola's first eleven.
Again, as with Grealish, whose £300,000 per week wages are potentially prohibitive to a move, Walker is also going to be on big money at the Etihad, and so if this report is correct, maybe Everton will want City to part-fund a loan.
Although he has a long and storied career with a sackful of medals won and is still a quality player, Walker is 35 and his very best days are surely behind him. Paying a substantial fee for him then would not appear to be a good decision.
Were he to become a Toffees player, Moyes' potential two first-choice right-backs could also have a combined age of over 70, assuming that Seamus Coleman agrees to another deal.
Such a situation seems far from ideal, as Everton need a long-term solution to their issues at right-back after a succession of failed attempts to find a player to replace Coleman.
Strangely, the Blues were also supposed to be tracking a right-back whose name bears a very striking resemblance to the England star: Kyle Walker-Peters of Southampton.
A younger player, he is available on a free transfer as his current deal runs out at the end of June, and he could well be ready to move on after the Saints were relegated from the Premier League. Given his relative youth and versatility, he would appear to be a better option.
Along with these names, the Toffees have been strongly linked with a succession of other full-backs, among them Vladimir Coufal, who, like Walker, is a very experienced international defender and one that David Moyes knows well from his West Ham days.
Despite the confidence of this report, we will of course have to wait and see if there is any such announcement by the club in the next day or so, and whether Walker will be making his way down the M62 from Manchester to Merseyside.