The Basque-born midfielder was one of Rafael Benitez's first signings when he took over at Anfield four years ago, arriving for £10.5million from Real Sociedad.
But Alonso, 26, has found his first-team opportunities limited with the arrival of Javier Mascherano and with young Brazilian midfielder Lucas also making an impact.
And with Benitez still trying to tie up the move of England international midfielder Gareth Barry to Anfield, the departure of Alonso would not be a surprise.
"It looks like his representative will arrive today," Cobolli Gigli said. "We can't deny that we're interested, but there's always the problem of getting value for money.
"(Managing director Jean-Claude) Blanc is working on this and on other possibilities."