Zaha has been linked with a big-money move to a host of top European clubs, including Manchester United, Chelsea and Borussia Dortmund.
Allardyce coached Zaha during their time together at Selhurst Park, and the 63-year-old believes that his former player should depart the club before the transfer window closes.
"He's ready because of the experience of Manchester United and then coming back to Palace and re-establishing himself as a top player," Allardyce told talkSPORT.
"A few years have moved on and he's established himself even more as one of the most talented players in his position in the league. The last two seasons, in particular, have shown his maturity, and his end product has got better. He's not only played out wide, but Roy [Hodgson] has used him through the middle successfully.
"It's London, where he prefers, so he'd be more comfortable there. So, as much as I don't like to say this to Crystal Palace fans who I love, it is probably time for Wilfried to move on, and get that next challenge under his belt. I do think the fee would have to be much bigger than what Chelsea are talking about."
Zaha has netted 21 goals in 113 appearances during his second spell with Palace.