Tottenham Hotspur were once again linked with a move for the winger, while a number of other top-six clubs were also thought to be monitoring his situation following a string of impressive performances in 2017-18.
No move materialised, though, and Zaha quickly put the speculation behind him with a goal in the season-opening 2-0 win over Fulham on Saturday before revealing that he is currently in talks with the club over a new contract.
"It makes no difference to me, because I had my head down anyway," Zaha told reporters when question about the rumours regarding his future.
"All that stuff was not going to affect me or how the team were playing. Whatever happens happens. But I'm all Palace - and you can see on the pitch that all I think about is the team doing well.
"We are still speaking about [a potential new contract], still negotiating, whatever. Just going to see if we can come to an agreement. The main thing for me is scoring goals. Everyone talks about 'no end product, no end product'. Well, tell me now."
Zaha's current deal at Selhurst Park runs until 2022.