The Brazilian forward, 20, joined the Bundesliga side in the summer on a season-long deal.
Frankfurt general manager Bruno Hubner now hopes that the Blues will allow him to remain in Germany for the 2015-16 campaign.
"Definitely, we will be looking to discuss things with Chelsea," he told Bild. "Chelsea might hand him another loan year at our club. That would be what we are looking for because I think the Bundesliga is currently the best platform for Lucas Piazon."
Piazon has scored one goal in five games for Frankfurt so far this season.