The Parkhead club are reported to have made enquiries about the Nigerian-born Swiss international however they face opposition from Serie A side Livorno.
The 24 year-old joined Siena on a permanent deal from French side Lorient for £2m in July and has scored 7 goals in 12 matches this season.
He rose to prominence with FC Zurich before moving onto FC Winterthur and Grasshopper.
It is understood Celtic are looking to sign Innocent on a permanent basis whereas rival suitors Livorno are currently only interested in a loan deal.
Celtic suffered a 2 - 0 defeat away to Shakhtar Karagandy in their Champions League qualifier this week with a lack of firepower up front one of the reasons attributed to the Scottish champion’s defeat.
Neil Lennon has struggled to replace striker Gary Hooper who departed for Norwich in the summer for a fee of around £5.5m.
The club’s bid to land FC Schalke’s Teemu Pukki appears to have stumbled following an injury to German side’s first choice striker Jan Huntelaar.
Heerenveen have also ranked up the fee for Alfreð Finnbogason to £5m which is outwith Celtic’s price range.