The 30-year-old DR Congo international left Posh this summer after making 252 appearances in two spells, having initially joined the club in 2008.
Zakuani won promotion from League One twice with Posh - in 2009 and 2011.
He was also in the Stoke side to finish second in the Championship in 2008.
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Northampton Town are close to agreeing a deal with defender Gabriel Zakuani following his release by Peterborough United, reports BBC Radio Northampton and BBC Radio Cambridgeshire.