The 30-year-old French defender is reportedly being tracked by Crystal Palace as Tony Pulis looks to complete a deal before the start of the new campaign.
However, he only has one year left on his current deal and the chance to play regular first-team football could see him make the switch to Selhurst Park.
He only made 18 league appearances for Lazio last season, and is thought to be available for around £1.2 million.
Pulis was keen to bring in Steven Caulker from Cardiff, but London rivals Queens Park Rangers won the race and have added the former Tottenham centre-back for £8 million.
Ciani is a cheaper alternative for The Eagles and his experience will undoubtedly improve an already solid defensive unit that kept 12 clean sheets in 28 games under Pulis last term.
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Caulker scored an impressive five goals last season, but played in 20 more games than Ciani, and the Englishman was more dominant in the air than the Lazio man.
Though the French defender won more tackles than Caulker and also made more interceptions and will certainly improve Pulis's backline further.