The Hammers have struggled at left-back all season and now look to have swooped for the experienced Romanian international, who has been with Shakhtar Donetsk since 2003
He has nine years' worth of experience with Ukrainian giants Shakhtar Donetsk behind him, as well as 88 caps for his national team, of which he is captain - including three appearances at Euro 2008, the country's last participation in a major tournament.
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However, their move to bring in highly-rated 31-year-old Rat has been confirmed by the player's agent Florin Manea.
"I am with Razvan in England, we are negotiating with the West Ham officials," Manea was quoted as saying by Romania's Sport.
"We will probably sign the contract on Monday. The trainer has put him on the top of the wishlist and the owner has approved the move."
The Romanian international had also reportedly attracted attention from Ligue 1 outfit Marseille.
Allardyce had promised West Ham supporters a busy summer in the transfer market, after signing an extension to his contract last week after the Hammers secured their position in the Premier League table.