The Italian international has five goals in 10 games for Juventus this season.
The Juventus man is not playing regular football in Turin and in a season where he will be hoping to feature for Italy in the European Championships next summer that is not acceptable.
Meanwhile West Ham have injury worries up front whilst Crystal Palace are in need of another striker.
Today has seen his agent Christian Maifredi conduct an interview with Tutto Mercato Web about his client's future.
He was even asked specifically about a potential loan move to West Ham or Crystal Palace in January.
This was his response:
"Already in summer there had been interest. When a player is in the national team and not play too inevitably targeted by clubs of major championships like the English.
"This no, there is at the moment no negotiations."
So it would appear that nothing is currently in the pipeline but the agent also made it clear that his player wanted to be playing regularly to assure himself of a place in the Euro 2016 squad next summer.
The Italian international had caught the eye during a co-ownership deal with Sassuolo last season. Juventus, the Italian champions, exercised their right to buy him permanently at the end of the season but he has played just 10 times for the club this season and has scored five goals, in an excellent return.
West Ham and Crystal Palace will be heartened by the news that Zaza is seemingly open to a loan deal.
But negotiations do not yet seem to be open and with a relationship already established with Sassuolo they would do well to get in front of this deal.