And Besiktas’ new coach Slaven Bilic is keen to grab the powerful defender to bolster his defence.
Bramble featured 19 times for Sunderland last season, but he did not get a game under current boss Paolo Di Canio.
He switched to the Stadium of Shite from Wigan for £1million in July 2010 and played 51 games for the Mackems.
He has been training with Ipswich Town to stay fit, but the Tractor Boys would only be interested in him if he slashed the wages he was on last season.
Any plans Besiktas had to offer Bramble Europa League football next season have been dashed.
UEFA have banned the Turks from the 2013-14 competition over match-fixing allegations.
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