Coyle has money to spend in Bolton's bid for Premier League survival after selling Gary Cahill to Chelsea and has already signed USA international Tim Ream.
Sky Sports revealed on Friday that the Trotters had made an approach for Zaha, who has been linked with a string of Premier League clubs in the past.
Speaking after Bolton's 2-1 FA Cup win over Swansea City on Saturday, Coyle acknowledged that the 19-year-old is the type of player who could improve his squad.
"I think there's players out there, and Zaha is certainly one of them, that I think would enhance our club for years to come on a permanent basis, and there are one or two on a loan capacity I'd love to bring in before the deadline on Tuesday," said Coyle.
"If it transpires then great, but it won't stop me targeting good, young players to bring to this football club that I think I can develop and make better, and that's what I'm trying to do."
Zaha only signed a new five-and-a-half year contract at Selhurst Park in December and Palace boss Dougie Freedman is determined not to sell during the transfer window.
Liverpool, Manchester United and Newcastle United have also been mooted as admirers of Zaha, but Bolton are reportedly ready to pay £5million to secure his signature.