The Uruguay international admitted on Thursday that talks were in place but refused to tell whether he would join Lazio or Genoa as both clubs were reported to be interested in a co-ownership deal.
Alfaro, who holds an Italian passport, is expected in Rome next week to undergo a medical examination and sign a four-and-a-half-year deal which will keep him at Lazio until the summer of 2016.
Meanwhile, it is reported that the Italian capital club are considering sending Alfaro out on loan to another Serie A side to allow him to get more games under his belt.
Lazio sit fourth in the Serie A standings, four points behind joint leaders Juventus and AC Milan, and travel to Siena on Saturday.
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