Reports emanating from Italy claim Juventus director general Jean-Claude Blanc has flown to Liverpool to discuss a deal for Alonso.
Juve have been linked with the classy Spaniard for some time, and now the Turin giants are ready to make an increased effort to lure him away from Anfield.
Alonso has suggested he was happy to stay at Liverpool, but he could be forced to rethink his position if Reds boss Rafa Benitez decides to listen to offers for the player.
It is believed the two clubs are in advanced talks about the move, but they have so far failed to agree a price with Liverpool holding out for £14million for the former Real Sociedad man.
However, Juventus are confident they can reach a compromise with Liverpool to see Alonso link up again with former Reds team-mate Mohammed Sissoko in Turin.
Blanc is also believed to have used the trip to England to hold talks with Chelsea over a move for Wayne Bridge.
Juve boss Claudio Ranieri is thought to be keen on signing on Bridge as he prepares for next season's Champions League campaign.
Ranieri is a big fan of Bridge having signed him during his time in charge at Stamford Bridge and with the full-back struggling to hold down a regular place in the side, Ranieri hopes the prospect of regular action at Juve could tempt him to leave England.