Everton chairman Bill Kenwright says he has “no concerns” over Ross Barkley’s £15m move to Chelsea.
The midfielder completed a deal with the Premier League champions last week, after turning down a £35m deadline day transfer in the summer.
Liverpool mayor Joe Anderson asked for an investigation to be launched on Tuesday over the transfer fee.
But in response, Kenwright said: “It was a deal we agreed because the boy didn’t want to play for Everton.”
Merseyside police have told BBC Sport that they have received a letter and are looking into the matter.
Anderson, who also wrote to the Premier League and Football Association, claims the reduced fee paid by Chelsea “represents a very poor deal” for Everton, as Barkley failed to feature for the Toffees this season.
The 24-year-old, who spent 13 years at Goodison Park, has not played for seven months because of a hamstring injury and had surgery in August.
Barkley denied he had turned down a last-minute move to Stamford Bridge following a medical, stating he wanted to “assess his options” in January.
Kenwright said on Wednesday that there were no issues with the deal for the England international, who had six months left on his contract.
“I’ve got no concerns at all, over what Joe said. I’ve got no concerns at all about Chelsea who were immaculate as they were in the summer, absolutely immaculate,” he said.
Barkley’s lawyer declined to comment.