Pantilimon, 24, impressed for FC Timisoara in last season's Europa League play-off against City.
City are thin in the goalkeeping department following the departure of Shay Given to Aston Villa and have only ex-Arsenal stopper Stuart Taylor in their squad as cover for Hart.
On his way: Costel Pantilimon (left) keeps out Man City's David Silva when playing for FC Timisoara in August 2010
Manager Roberto Mancini hopes to complete a deal for Pantilimon, who has 13 caps for Romania, before Sunday's Community Shield clash against Manchester United.
Pantilimon is highly-rated across Europe and has previously been linked with Inter Milan and West Brom this summer.
Romania's No 1: Pantilimon is highly rated across Europe
FC Timisoara, who finished second in the Romanian top flight this year, were relegated due to accumulated debts.
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Source: Daily Mail