The report has claimed that Leeds, who are aiming to clinch automatic promotion from the Championship to the Premier League at the end of the season, made an enquiry to sign the former Newcastle United striker.
Brentford, who are also in the hunt for promotion to the English top flight, were interested in the 24-year-old as well, according to the report.
However, the Whites and the Bees reportedly cooled their interest once they were quoted the transfer fee by the Posh.
Peterborough director of football Barry Fry has told The Peterborough Telegraph that Toney “wanted to leave once he became aware of interest from higher-level clubs”.
According to BBC Sport, Toney scored 24 goals and provided five assists in League One for Peterborough this past season.
Renewed interest from Leeds United?
With Leeds looking likely to get promoted to the Premier League for the 2020-21 campaign, the Whites will need a new striker even though Patrick Bamford is playing well at the moment, and perhaps the West Yorkshire outfit will make a move for Toney again this summer.