Santa Cruz has been cleared to leave Eastlands after playing under half an hour of Barclays Premier League football for Roberto Mancini this season.
The Paraguay international would prefer to stay in England, with his former boss Mark Hughes keen for Fulham to agree a deal, while there has also been interest in Germany from Wolfsburg and Werder Bremen.
Italian job: City striker Santa Cruz (right) is attracting interest from Serie A
AC Milan were keen, but are instead close to completing a deal for Antonio Cassano to join from Sampdoria in January.
Lazio coach Edy Reja has asked for a top-class striker in January to stay in the Serie A title race.
His side are just three points behind leaders AC Milan, but do not have a stand-out forward to shoulder the goalscoring burden, with erratic Mauro Zarate returning just four in 16 games.
Lazio were close to an initial loan for Santa Cruz in the summer but the deal hit a hitch at the last minute.
The Rome side have since looked at other options but are returning to the 29-year-old as the most easily achievable deal.
Nicklas Bendtner was sounded out but says he will stay at Arsenal till the end of the season before reassessing his options.
Werder Bremen's Hugo Almeida was Reja's preferred option, but Lazio fear that the Portugal international has already virtually agreed a move to Besiktas.
A sticking point in a move for Santa Cruz could be reports from Italy that Inter are considering a shock move to give them cover up front.
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