The Premier League duo have both been linked with moves for the unattached forward, who was released by Schalke at the end of last season.
But, La Viola have now entered the race after losing summer arrival Mario Gomez to injury.
The German international is facing a lengthy spell on the sidleines with a knee injury, which has forced Fiorentina to explore the possibility of a new signing.
With the transfer window closed, Marica is one of the few options available to top sides across Europe, with his status as a free agent meaning that a move could be completed at any stage.
The 27-year-old is believed to be on Arsene Wenger’s radar, with the Frenchman desperate to bring in a new attacker to bulk out his squad.
Meanwhile, the Hammers are also keen, but Sam Allardyce may instead look to re-sign Carlton Cole – whom he released over the summer.
Despite being without a club, Marica is still regarded as a top attacking talent and is a part of the Romania squad.
Should West Ham or Arsenal move for Ciprian Marica?
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