Johnson joined QPR at the start of last season but missed the majority of the campaign due to a cruciate ligament injury, managing just four appearances in all competitions.
The former England international has scored two goals in four games for QPR so far this season, alerting him to Premier League new boys Crystal Palace.
"We have made a bid for Andy Johnson we are waiting to hear, that would be a permanent deal," Palace chairman Steve Parish told BBC Sport.
"We are trying to get someone else in on loan and we are trying to buy another one as well."
Johnson spent four seasons at Palace between 2002 and 2006, scoring 85 goals in 160 games.