Konchesky, who is currently at League One club Gillingham, has reportedly fallen out of favour at the club.
The 35-year-old, who has played for nine different clubs including Liverpool, is joining Billericay according to the Basildon, Canvey and Southend Echo.
The club’s owner has been teasing a significant signing with the phrase 'bigbigbiggun' on Monday and Tuesday.
Barking boy Konchesky has made 29 appearances for the Gills this season, but has fallen down the pecking order under new boss Andy Pennock.
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