The versatile Swiss international could join Serie A side Fiorentina within the next 48 hours, according to Italian daily Corriere dello Sport, with the two clubs set to reach an agreement.
The Hammers rejected an opening £3.1million offer from the Italian outfit last week for the 25-year-old, standing firm on their £4.5m asking price.
Is this the way to Italy? Valon Behrami is said to be joining Fiorentina
But with unsettled Behrami desperate to head back to the country he left in 2008 to join the Hammers - he signed from Lazio for £5m - the clubs are close to reaching a compromise.
'We are hopeful,' Fiorentina club administrator Sandro Mencucci told Italian TV station Rai 3 last week. 'But until he [Behrami] is in Florence and he has signed, we cannot be sure.'
Behrami's pending departure would release vital funds for West Ham as they look to bring in fresh blood to boost their top-flight survival chances.
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