They are split equally between the Premier League and the Championship, according to Posh director of football Barry Fry, although no concrete bids have been received.
The list of clubs chasing Toney does not yet include Watford despite a tip-off to the Peterborough Telegraph they were preparing a bid.
However Fry, who has revealed Posh are lobbying for an extended transfer window to run from the start of the new season through to January 31, did not dismiss a recent report in a national newspaper that Brighton were one of the clubs to have contacted him.
“Ten clubs from the Premier League or the Championship have asked about Ivan since we stopped playing,” Fry revealed.
“But none have made a bid yet as most of them don’t know what division they will be playing in next season, how much money they will have to spend and the transfer window isn’t even open for English clubs.
“Watford are not one of the clubs to have contacted me, but maybe they will because I see a lot of clubs at the bottom end of the Premier League and the top end of the Championship who don’t have a regular goalscorer.
“Ivan guarantees goals which makes him a very valuable commodity these days.
“Clubs know how much we want and we will have to wait and see if anyone bids it.”
Posh are believed to want a fee in the region of £10 million for Toney who scored 26 goals in a shortened 2020-21 season. It’s understood they turned down an offer of £8 million in January from Championship promotion contenders Brentford who remain interested in the 24 year-old.
West Brom, who are also interested in former Posh striker Dwight Gayle, are another club expected to make a move for Toney.
Other clubs linked with a raid for Toney are Celtic, Rangers and New York Red Bulls.
“It’s all a bit pointless while the transfer window remains shut,” Fry added.
“Clubs can bid what thay want and make all the enquiries thay want, but they can’t sign anyone which is ridiculous.
“We have lobbied the EFL to get them to ask FIFA to change the transfer window so it runs from the start of the season to the end of January without a break.
“Selling players could be the difference between life and death for some clubs right now so an extended window for one season makes a lot of sense.”