I would laugh if the Ficantieri bring the FREMM EVO on board and win actually.
They got the US background for the Constellation-class, had (not the best) experience with the US Navy way of thinking, so in many ways they are in good position. The FREMM itself is mature design, do the job, but the EVO is new version, which provide some risk in the table.
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I would bet second to the South Koreans. They on the roll to get the necessary naval infrastructure in the US soil, they have the Chungnam-class frigate, which I would call the weak point of the offer, but that's my personal taste. What South-Korea had difficulty is to prove their capabilities (yea, I know the Ficantieri too has this problem with the Constellation-class...). They probably the dark horse still in this race...
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Japan maybe maybe the strongest contributor, the Mogami is more than fit for the role, they prove more than impressive their building scale and export commitment with the Australian frigate tender. But Mitsubishi does not have any ground in the US military naval build - yet they have good relations to the US Navy, like in the US ship repairs in japan.
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The BAe Type-26 is can be a contender, dedicated ASW frigate with good backwind of the BAe zillion connections with the US higher ups. What it's weak point it's maturity, which is nonexistent, so they perhaps cannot even put in the start line.
What is interesting question is the other notional options. The Babcock Arrowhead 120/140 probably a cheaper alternative, but I hardly seen a strong contender placed next to the other potential alternatives, and actually it's not a mature design, just as the Type-26.
Perhaps the french try their luck with the FDI, and even the germans the MEKO 200, those are mature designs, but they don't really have the right connection level to the higher ups to get serious chance...
But that's only my week eyed insight...