The 25 year-old has performed well for Posh on loan from Huddersfield in each of the last two seasons, racking up 55 appearances and scoring two goals.
But Brown is due a big pay bump at Huddersfield next season and Posh are unwilling to match it.
Posh director of football Barry Fry said: “Reece has been brilliant for us, but we think we can do better for the money.”
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Fry has contacted Leicester City about the availability of Josh Knight another player to have spent time at Posh on loan recently.
Leicester have just taken up the option of an extra year on Knight’s contract. The 23 year-old can play in midfield or central defence.